h1b transer

Before my previous H-1B expires (Jun 3,2005), my current employer filed h-1b transfer petition for me on May 25 and told me I can start new job on June 1.
I have got my first paycheck from current employer on June 30 but did not get H-1B approval yet( note: my previouse H-1B has been expired). I am worried about my working eligibility.

Could anyone who has same experience give me some advices, please?

Thanks a lot