How does a delta wing deal with supersonic boundary separation?
1. Aeroelasticity
Unlike a tailplane, a delta wing is more rigid due to its much bigger chord and multiple spars, so control reversal due to aeroelasticity isn't a special concern.
Big subsonic jetliners typically lock the outer ailerons at high speeds. Concorde featured a similar function for the outer elevon, but only if $V_{MO}$ is exceeded by 25 knots as a safety measure (flight manual page 09.01.03).

Concorde's structure also makes it much more resistant to the distorting forces of supersonic flight than aircraft built before her. (...) If Concorde gets substantially above its design speed, the outboard elevons are automatically neutralized, so that no twisting is possible (heritageconcorde.com).

2. Transsonic separation
Delta wing aircraft rely on thin airfoils (vs. blunt) where the pressure gradient is more forgiving. And due to the bigger chord, the elevons deflection doesn't result in a big camber change as happens on the smaller tailplanes. The big sweep angles of delta wings also make the airflow see thinner airfoils, making the transition to supersonic easier.
3. Supersonic separation
Not an issue since the shock wave moves to the trailing edge at supersonic speeds.

Source: https://history.nasa.gov/SP-367/f87.htm

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