untimly filed H1B

My old H1B visa was expired on Aug. 31, 2003 and I just get approved notice of the extension in Oct. However, I got another job offer during my visa extension period (only got receipt notice of the extension). The new employer filed the H1B transfer for me on Sep. 10, 2003 (the extension was not approved at that time), I was told, which might be considered as untimely filing according to the BCIS rules. The new employer urged me to work, because they thought it should be all right for me to work for them.

I am thinking if the premium processing is needed to ensure everything O.K. just in case BCIS still considers my new H1B as untimely filing even though I have got approved H1B extension already. Meanwhile, new employer requires me to travel oversea due to business reason. I’d like to know how to resolve this issue. Thanks a lot.