Is my charge controller working like it's supposed to?
Ask the manufacturer whether this is normal behavior.  That really should have been obvious.

If you blew the fuse in your multimeter, replace it.  That again really should have been obvious.

All that said, my guess is that something is wrong.  Whatever is supposed to detect that the battery is fully charged may not be working right.  14.8 V is very high for a "12 V" lead-acid battery.  That's about a volt more than typical float charge voltages.  It is quite possible that your battery is being abused.  Not only will its life be significantly shorter than it should be, but it could be releasing dangerous combustible gasses.

Again, contact the manufacturer, especially if the unit is still within its warranty period.