Absolutely not. The previous employer has no role at all and does not even have to know it happened - you could apply for a H1b transfer, get it approved, decide you don't want the new job and continue working for your old employer without them ever knowing you had looked around. Everyone I know has had the transfer completed before giving notice at the old job so that if it somehow is denied (eg new employer does not have a job that qualifies for a H1b), the current employer doesn't have to know you wanted to leave.
But the USCIS generally approves petitions to change from one employer to the next if the gap between jobs is short. 30 days is acceptable