Nope, that's completely normal.
As long as it's putting out more than the battery voltage shows with the engine off (full charged battery should show between 12-12.4) , and your battery isn't getting squirrelly, I wouldn't worry about it that much.
Higher output after starting is normal, it's recharging the battery after the drain of cranking.
Also, factory gauges are notoriously inaccurate, no matter the make/model. If you really want to see what the charging system is doing, hook a voltmeter up to the fuse panel (any hot circuit will do) and get some readings there, then compare to the dash gauge for future reference. That'll do 2 things: 1 give you an accurate reading (assuming a good voltmeter), and 2. give you a reading far enough away from the alternator / battery to account for voltage drop along the wiring lengths). But this is all starting to border on obsessive - not that I've ever done anything like that, lol.