I am not aware of any Islamic tradition that says Muhammad claimed to be praying to the Al Aqsa Mosque before they started praying to Mecca. The only reference I am aware of that is attributed to Muhammad is in the night journey, which does not identify a location for the Al Aqsa mosque. That came much later. There is an Islamic tradition that Muslim scholars at the time of Muhammad debated whether the Al Aqsa mosque was either somewhere in the vicinity of Mecca or in heaven.

"Islamic tradition" consists largely of direct quotes: Muhammad said this or that, or one of his companions said this or that about what Muhammad did. "Islamic tradition" itself does not say these things in a vague omnipresent sense, it is the collection of the quotes.

Are you just making it all up as you go along? It's almost like you are doing what Muhammad did - trying to invent your own version of Islam, with everyone else thinking your interpretation is juvenile and ignorant. There are huge volumes of references to what Muhammad actually said and did, which Muslims and Islamic scholars are fairly anal about referring to, but you expect us to take your word for it, with the only evidence you are able to present being a vague claim about it "corresponding".