Thats a CRAZY high climb rate!
Your bird-dudes are flying above the range of a 14.5mm aircraft cannon, which has a maximum engagement cieling of 4,000 meters. These creatures can sustain muscle powered flight for 90 seconds, during which period they are reaching this altitude. This means they are going to be climbing at 44 meters per second, giving them a climb rate of about 8,800 feet per minute. For reference, this is almost the same climb rate as the F-86 Sabre jet fighter.
I'd probably tone that down just a weeeee bit. Perhaps their flight method is more akin to an albatross or a condore where they slowly circle riding thermals to gain altitude, then glide from there. Because otherwise you have bird people with the functional climb and speed capabilities of 1960's era jet aircraft.
That aside, Heres how to use them:
Commanders can now command units much farther afield than they normally could. A commander now no longer has to keep his entire army within riding distance. He can, using these swift couriers, divide his force up among multiple strategic positions, and use them to attack or react much more fluidly. Real Medieval commanders could not conduct strategic small unit manuevering. The best they could do was to send out small raiding and harassment parties and trust thier commanders to do the best. This was unpredictable, and if unlucky, a loss or critical info might not reach him until it was too late to utilize said info. Now, commanders do not have to worry about this and can conduct highly mobile, decentralized strategic actions.
Part of that reaction speed means that he can know the disposition of enemy forces well before hand and plan his responses in advance. Instead of having to wait until they are right on top of him to eye them up, he can set ambushes, destroy infrastructure in front of them like bridges, or close mountain passes. This means a commanders ability to manipulate the conflict enables him to better set the pace of the conflict and attempt to funnel the enemy into a position of his choosing.
Perhaps a commander could sow dischord in enemy rear areas by dropping propaganda leaflets on enemy cities and villaiges. Tell them thier armies have been crushed, or thier charismatic leader has fallen. Panic the public with conflicting reports and false narratives.
Fire was a real threat for medieval cities. You could use a few dozen of these bird men to fly in under cover of darkness, start a bunch of fires, then fly away. With luck and skill these fires may rage out of control and cause incredible economic and infrastructural damage to an enemy's rear areas. This forces the enemy to use forces he might otherwise have been able to commit to battle for defending his own assets. Additionally, damage like this is going to make a war far more expensive, and further diminish the number of assets that he could bring to bear on the front.
Dress up some of your bird-men to look like some of the enemy's bird-men and have them carry messeges disguised as official orders to enemy commanders. Order units into ambushes, or give them orders to move to some location in the middle of nowhere where they miss a battle, or even, if you are insaneley lucky, convince them a nearby unit has been discovered to be traitors and to attack them.