H1B Transfer - Start working for new company when checks cleared. Problem?

A new company started the H1B transfer process, and as soon as the fees checks cleared with USCIS I was instructed that I could start working. The actual receipt came in about a week later.

Do you guys see an issue with that?

One can start working as soon as the petition is received by USCIS. I don’t see any issue in your case. The only thing you need to watch out for is denial of this petition. In that case, you need to return to old employer or immediately have another employer file H-1 petition for you.