Air carrier Captain reported during the climbout they got a traffic alert from an aircraft 500 feet below them. ATC directed them to turn left to avoid traffic that was on a runway heading on the parallel runway.

Narrative

We took off from runway 15L with instructions to turn left heading 360 degrees from ATC. The FO was PF (we were conducting FO IOE). During the climbout at 600-650 feet AGL based on the CA side radar altimeter; which was around 800-900 feet MSL) we got a TA that advised us of vertical speed. The FO was hand flying and Autopilot was not engaged; as we did not reach acceleration altitude. I noticed the intruding aircraft on the TCAS screen showing 500 feet below us. The FO followed the TCAS alert and command. After we were clear of the conflict I advised ATC (tower) that we responded to a TA; and they said; 'we had an aircraft on runway heading on the parallel runway and had given you a turn to the left; and that we had both of you in sight from the tower.' It seemed to us based on our ATC communication that they were aware of the separation and had both of us in sight visually. We continued the flight with no further incident.Suggestions: The only thing that we could have done better was getting our turn earlier; instead of waiting another 100-200 feet to turn. However; even with a delay of a turn with those margins of a couple hundred feet; there shouldn't have been a TA or any sort of separation conflict.