I'm about to buy a secondary fermenter (generic plastic bucket and drill a hole to fit in a plastic bottle filler) for the usual reasons. I'm, however, curious how would I go about and clean the little bottler and tap? Will I have to pop it out every time I use it?
Yes, if it can be taken apart and reassembled without damaging it. I would disassemble clean and store. Then sanitize and reassemble the valve and sanitize the bucket as a whole before use.
A clean sanitary fermenter and it's parts is critical. This is where your wort is most vulnerable to infection.
Line brushes are useful if the valve doesn't come apart. Rotate the valve shutoff and clean it in opened and closed positions. Like a revolving door areas to harbor infection get sealed off in different positions. Any wort debris left behind can negate sanitation.
I would advise popping it out and cleaning it every time, cleanliness is next to godliness or at least next to not having contaminated beer.