When Chris Carter created Millennium, he was very clear that Frank was not psychic. To firmly establish this from the start, when writing the pilot he made Bletcher ask Frank directly "like a psychic?" Frank's response is a firm, unequivocal "No."
The stuff about Frank's mother passing on psychic ability was all established retroactively in S2. Glen Morgan and James Wong, who had no part in creating the series, remade things in their own image when they took charge. The episode in question, "Midnight of the Century," was written by a pair of writers new to the industry (Erin Maher & Kay Reindl) who were hired and nurtured by Morgan & Wong. They wanted to do things differently.
Hope that clears things up.
(Take a look at this if you're interested in reading more.)