Unfortunatly this is not possible to save anywhere. I have checked and found a few Enhancement Requests. Normally I would say, Submit one as well so it's added to the list, but I checked in NX 11.0 and this option has been removed. I have quickly checked and the default behavior is now as you prefer it.
It starts filtering as soon as you type, and "contains characters you type".
I hope this answers your question?
Dennis de Brouwer Application Support Engineer GTAC EMEA - Siemens Industry Software