No they don't.
Edit: Not since 2016
Edit: this is supposed to be a professional forum right? I'd think most people are exactly aware of where to find ICANN and their policies.
Verisign locks domains for two month after registration.
GoDaddy and other used to lock domain on a registration change, then added a way to override the lock. According to Godaddy's documentation, all domains are locked after a transfer or registration.
Big question, were your domains registered or transferred to Epik in the last 60 days? Sorry if I missed that info.
** found it:
"I have another thread here about an expired domain purchase. Same issue, support won't unlock my domain."