They are a people that follow Muhammad Ilyaas, the founder of this Jamaa’ah.
A biography of the founder: Muhammad Ilyaas was born in 1302H. He memorized the Qur’aan and read the Six Collections of Hadeeth.  He was upon the Deobandi methodology, taking the Hanafee madh-hab, the Ash’aree and Matureedee Creed and the Sufi way. They have four Sufi orders amongst them:
1. The Naqshabandees
2. The Sahroordees
3. The Qaadirees, and
4. The Jishtees
Shaikh Muhammad Ilyaas gave the Sufi bay’ah (oath of allegiance) to Shaikh Rasheed Al-Kankoohee, who later became Shaikh Rasheed As-Saharanpuree. Then he renewed it with Shaikh Ahmad As-Saharanpuree who certified him to take oaths of allegiance. Muhammad Ilyaas would sit in detached isolation (khalwah) by the grave of Shaikh Nur Muhammad Al-Badaayunee, in what is known as the Jishtee Muraaqabah (self meditation). And he would go out to the grave of ‘Abdul-Qudoos Al-Kankoohee, the one who forced the ideology of wahdat-ul-wujood  on him. He resided and taught in Delhi and passed away in 1363H.
Circumstances that brought about the start of the movement:
Shaikh Abul-Hasan An-Nadwee saw that Muhammad Ilyaas took refuge in this way of giving Da’wah when the ways of blind-following failed to rectify the people of his region. Shaikh Miyaan Muhammad Aslam quotes one of Ilyaas’ sayings that he received kashf (mystic disclosure) to follow this way through a dream in which he was inspired with a new tafseer (interpretation) of Allaah’s saying: “You were the best nation brought out for mankind, commanding good and forbidding evil and believing in Allaah.” [Surah Aali ‘Imraan: 110] And it was that going out (khurooj) to call people to the way of Allaah cannot be realized by staying in one place based on Allaah’s word “brought out” and that one’s Eemaan increases by going out in this khurooj based on Allaah’s saying: “and believing in Allaah” after having said:“brought out for mankind.”
The following can be noted from what has just been mentioned:
1. The Qur’aan is not interpreted by makshoofaat (mystical disclosures), and by Sufi dreams, of which the majority of them, rather all of them come from the inspirations of the Devil.
2. It is apparent from what was stated previously that the founder of this Jamaa’ah was engrossed in Sufism from head to toe. This is because he gave two oaths of allegiance on it and was tested by its false beliefs and because he would spend his time sitting by the graves of Sufis.
3. The founder of this Jamaa’ah was a qubooree (grave worshipper) and a khuraafee. This is clear from his saying: “…and he would sit in detached isolation (khalwah) by the grave of Shaikh Nur Muhammad Al-Badaayunee.” And concerning the second person, he mentioned that he forced the ideology of wahdat-ul-wujood on him. So his being attached to the grave of the one who forced the ideology of wahdat-ul-wujood on him is without doubt a clear proof that he held that same belief
4. Those who believe in wahdat-ul-wujood claim that Allaah embodies Himself inside the attractive woman – and refuge is sought from Allaah! This is a matter that has reached the highest level of repulsiveness. May Allaah give them what they deserve of His curses and wrath!
The methodology of the Jamaa’at-ut-Tableegh can be summarized in six issues or six principles or six characteristics:
1. Actualizing the statement of Tawheed: “Laa Ilaaha Illaallaah Muhammadur Rasoolullaah” (There is no deity worthy of worship except Allaah and Muhammad is His Messenger)
2. Praying with full submissiveness and humility
3. Knowledge of the Virtues (Fadaa’il) and not the Fiqh issues (Masaa’il) along with knowledge of dhikr
4. Showing generosity to the Muslim
5. Correcting the intention
6. Calling to Allaah (i.e. Da’wah) and going out (i.e. khurooj) for that purpose in the Way of Allaah upon the tablighi manhaj.
There is an objective behind each of these six principles or characteristics as well as a virtue to be attained. So for example the objective behind (Laa Ilaaha IllaAllaah) is to: “Eradicate the corrupted yaqeen (Certainty) from the heart while placing the correct and valid yaqeen into the Essence (dhaat) of Allaah.” They really intend the belief of wahdat-ul-wujood with this.
Point to be noted about Jamaa’at-ut-Tableegh:
1. The founder of this Jamaa’ah was raised upon Sufism and gave two oaths of allegiance on it.
2. He would position himself by graves, waiting to receive Kashf (Sufi mystical disclosure) and meditative ideas from the deceased inside them.
3. He would perform the Jishtee Muraaqabah (self meditation) at the gravesite of ‘Abdul-Quddoos Al-Kankoohee, who used to believe in wahadat-ul-wujood.
4. The Jishtee Muraaqabah is to sit by a grave for half an hour of every week, covering the face and reciting this dhikr: “Allaahu Haadiree, Allaahu Naadhiree.”  This statement or this action if done sincerely for Allaah is an innovation. And if it is done for the person in the grave then it is committing Shirk with Allaah. And the last of the two is what is most evident.
5. They have four of their graves located in the masjid from where their Da’wah emerged.
6. The founder of this Jamaa’ah believed in Kashf.
7. The founder of this Jamaa’ah was a grave worshipper.
8. The Tablighis perform their worship with an innovated form of dhikr, done in the way of the Sufis. This is by splitting up the statement of Tawhheed (Laa Ilaaha IllaAllaah).
9. Whoever cuts off the negation part of the Statement of Tawheed from its affirmation part intentionally, by saying “Laa Ilaaha” (only), then this necessitates the fact that he has committed disbelief. Shaikh Hamood At-Tuwayjiree stated this, quoting it from the scholars.
10. They make it permissible to wear amulets that have on them mystical writings and names of unknown people, which probably are names of devils! And this is not permissible.
Source: Al-Ibaanah eBook – Modern Day Deviant Groups : Shaikh Ahmad bin Yahyaa An-Najmee