After the defeat of Aybak and Yildiz in 1206, the last two slave generals of the Ghaznadian Dynasty, the Roma were free at last after almost 200 years of slavery. Free, as far as that was possible at this time.
Around the year 1200, the complete region had been converted to the Islam, even the native country of the Roma. Though many small Arabic emirates were founded after the collapse of the Ghaznadian Empire, the Roma did not have this option because they did not have any territory to claim for themselves.
This was the reason why the Roma joined the Empire of the Rum-Seldchuks. The Rum-Seldchuks offered the conversion to Islam with the incorporated advantage of becoming citizens. Muslims did not take Islamic slaves, thus this was the way out of slavery for the Roma.
The Sinti, on the other hand, seem to have refused to join the Islam and thus remained in slavery. This circumstance led to the differentiation between Roma and Sinti, starting from the Sinti.