About the usage of the word Ummah
أُمَّة in Arabic refers to a community of people of mainly common descent, history, and language; a tribe or confederation of tribes it could therefore mean people, nation, any kind of community or all people all nations or a part of a community according the context.
So basically you could say that Ummah is a term of wide comprehension. As it can gather together and/or separate at the mean time.
For example you could call the staff in your company an Ummah. You could also call all Muslims alive one Ummah. You could call Muslims an Ummah. YOu could call your family Ummah and you could call all chess players an Ummah etc.
So based on that each Prophet of course had an "own" Ummah. I think this already should answer your question.
Examples from the Qur'an
With this meanings you may find it also in the Qur'an (the English synonym used is put in bold letters, in cases with the restriction meant):
- Our Lord, and make us Muslims [in submission] to You and from our descendants a Muslim nation [in submission] to You. ...(2:128)
- That was a nation which has passed on. ... (2:134 and 2:141)
- And thus we have made you a just community that you will be witnesses over the people and the Messenger will be a witness over you. ... (2:143)
- Mankind was [of] one religion [before their deviation]; then Allah sent the prophets as bringers of good tidings and warners and sent down with them the Scripture in truth to judge between the people concerning that in which they differed. ... (2:213)
- And let there be [arising] from you a nation inviting to [all that is] good, enjoining what is right and forbidding what is wrong, and those will be the successful. (3:104)
- You are the best nation produced [as an example] for mankind. ... (3:110)
- They are not [all] the same; among the People of the Scripture is a community standing [in obedience], reciting the verses of Allah during periods of the night and prostrating [in prayer]. (3:113)
- So how [will it be] when We bring from every nation a witness and we bring you, [O Muhammad] against these [people] as a witness? (4:41)
- And We have revealed to you, [O Muhammad], the Book in truth, confirming that which preceded it of the Scripture and as a criterion over it. So judge between them by what Allah has revealed and do not follow their inclinations away from what has come to you of the truth. To each of you We prescribed a law and a method. Had Allah willed, He would have made you one nation [united in religion], but [He intended] to test you in what He has given you; so race to [all that is] good. ... (5:48)
These are a couple of examples of the use of Ummah in the Qur'an (there should be around 40 on the whole) which show that Ummah may refer to a part of a bigger community, a whole community or a whole nation.