Call them back to address it, you are right it is not normal.

Thank you. I will look into it. I was pretty sure I was correct. thanks for your time.

The 1% win's this time,fan continue's on heat but go's off with compressor while cooling. You make an interesting point however. A determined gearhead could jury rigg fan to run a few secounds longer purging cool air from ducts. If fan were to run too long,circulating air could start picking up heat if ducts were in attic.

@klem1 I honestly did not understand your comment :-( I don't understand what the 1% means etc. No clue sorry :-(

@weedmeister Are you saying I have nothing to fear with my A-Coil freezing up ? I just thought that if the compressor and fan go off exactly at the same time, that coil in the furnace would be so cold it would even become colder because the fan has stopped blowing and bingo, it freezes or explodes or something like this. The installer had told me that the an A-Coil can freeze. I didn't understand what situation he was talking about though and it wasn't about the fan turning off too quickly. He was just talking in general about past experience with somebody he installed a new one for.

" I'm 99% sure this is NOT correct."

100 -99= 1 :-)

LOL Klem that was a good one.

fan shuts off on AC with compressor so it doesn't add humidity back into the house. (water on coil or water sitting in pan could be reintroduced to the house as humidity.)

If the furnace is running... completely different operation.

I agree with weedmeister. Doesnt make sense for it to stop right away while the coil is still cold. I dont think it will cause damage but it just doesnt make sense. The amount of humidity that would possibly go back into the house is minuscule. 30 secs sounds about right to get the supercold into the house instead of just sitting there on the evap coil. I know mine doesnt stop right away.

Many systems are set up where fan continues to run for a set time on heat and no run time on cool. This is usually determined by dip switch setting on the control board.

As others have said ... the behavior during cooling depends on the individual system and how options that may be available are set. The first two houses and one apartment in which I've lived had systems that shut the blower off immediately. My current house (built in 2004, Carrier system) runs the blower for an additional couple mins. All the systems at the business where I've worked (three systems 30+ years old, one 2 years) shut the blower off immediately.

The coil will not freeze-up if the blower stops. Heat extraction/transfer stops when the compressor shuts off so the coil will not get colder than it is at the moment the blower stops running.

The OP said "Just had central air installed, and I noticed ". Several answers have been offered leading us to believe no two air handlers are the same. If you just had it installed Beerman surely you still have the owner's manual and if not,ask the installer to give you one. The answer to your question and several others you might have later should be in the manual. That is unless there's room for more possibilities. In that case I heard of a blower that would run on and on until the old lady whacked the handler with half a brick to make it stop.

Since this is new and it is a Trane, I think they have this feature called 'ComfortR' or some such that is a switch setting in the furnace. It depends on the model. Mine is variable speed and will run a profile for shutdown that reduces fan speed over time.

Shutting off immediately will not 'hurt' the coil. That's how older systems used to be set up.