Some refugees were said to have been put on wanted lists by the YPG, the armed forces of the Syrian Kurds, as suspected collaborators with Isis.
"International coalition jets are bombing now," Yisr al-Khoder, a Tel Abyad resident now on the border said.
"There are 3000 civilians crowding the border, waiting to pass into Turkey. Some are afraid of being arrested by the YPG, and some are fleeing the heavy bombing."
He was on the Turkish side, but said his brother and his pregnant sister-in-law were waiting to leave.
The Syrian Kurds have begun a major fightback in recent months against Isis in both Kobane, the town in central northern Syria that was subject to a bitter battle between the two sides from the northern autumn last year, and in Hasake in the far northeast.
Now the two separate Kurdish "cantons" have pushed their frontlines to a point where they are nearly surrounding Tal Abyad in between. They are hoping to create a long "safe haven" for Kurds and others from both the regime and Isis.
Al-Khoder said the Kurds were now less than 3km from the eastern entrance to the town, but that Isis militants were digging in and gave every appearance of not wanting to give up without a fight.
The YPG said it was at the eastern approaches to the town, just 80km north of Raqqa, which Isis took over in 2013.