They did arm their own cavalry with muskets, as I'll explain shortly. The reason they didn't arm the Crimean Tatar cavalry with muskets is quite simple: because those cavalry weren't theirs, they were Crimean. The Crimean Khanate was its own state with its own forms of military organization; the Ottomans couldn't delegate a particular style of equipment or tactics for them to use. In Ottoman campaigns, the Crimeans acted as an auxiliary force under their own independent command. They performed reconnaissance, raided and looted enemy territory, harassed enemy forces in an effort to sow confusion, and screened the main Ottoman army on the march and during sieges. These were crucial functions for which the Crimean light cavalry were especially well suited, even if they couldn't be expected to directly engage with a large infantry formation with much success. The Ottomans had other forces for that purpose. So long as the Crimeans were able to fulfill these auxiliary functions effectively, there was little pressure on them to adopt a different style of equipment.

When it came to directly engaging hostile field armies, first and foremost in the Ottoman repertoire were the Altı Bölük Halkı ("People of the Six Regiments"), numbering roughly 15,000 members in the seventeenth century. These were the cavalry equivalent of the Janissaries, the salaried household troops of the Ottoman Sultan, and they acted as the Ottomans' premier shock troops for cavalry charges. They appear to have gradually adopted firearms around the beginning of the seventeenth century, with the typical tactic being to fire them once at the beginning of a charge before closing in with sword and lance. In addition to the standing Altı Bölük formations, the Ottomans also employed mercenaries called sekban or sarıca that functioned like European dragoons or mobile infantry, carrying long muskets and using their horses for mobility, dismounting to fire and reload (I've written about the origin and nature of these mercenaries here). So the Ottomans certainly didn't neglect to incorporate firearms into their cavalry tactics where appropriate.