The argument is:
'does asking me to let him stay count as giving financial support because it was housing without really paying'
The answer is clearly no.
Judges look at intentions.
Giving 'financial support' is not the same as intending to support someone for the rest of their life. Therefore your Aunt asking if he could stay in your house does not make him her legal dependent with a claim on her estate.
Definitions in laws have meanings. Either he is legally dependent or he isn't.
You cannot just say that because someone helped you out once that makes you a legal dependent entitled to claim on their estate.
I can't understand why your solicitors have not already assured you that he has no claim.
He is not going to take this court because he knows he will lose. He doesn't want to go to court, he just wants you to let him live in your house. Once you have evicted him I'm pretty sure he'll just go away.
Definitely continue to ignore his calls. Mute or block him. If there is any actual action from him his solicitors will write to you. Just try to forget about him now, this will soon be over.