If the domain was from an expired auction than, after you made payment, the status will say "processing" for 3-4 days. This is normal, it doesn't mean your payment is processing, it just means the domain is processing.
If you purchased a new domain and it still says "processing" after you made payment then yes that's something Dynadot should assist you with. Normally payments for new domains are instant (unless it's the very first time you purchased a domain and then ID verification may be in order).
[This post has been edited by b_c_heusden_be on Oct 8, 2012 12:34am.]