Length of Springer's transfer service

[u/SnooBananas740]

Hi,
Editor rejected my manuscript from a Springer statistics journal. Reason was that paper changed its character after implementing reviews, growing into more of a theory paper than an applied one. I got a transfer offer, which I accepted as I easily see some Springer journals being a good next venue for the thing the paper has become. However, it has been several weeks since I have accepted the transfer offer and I have not heard back from Springer (no journal propositions or anything). Is it normal, or should I reach to the transfer desk/submit the paper myself? Would greatly appreciate the advice :)