Relay switching AC/DC plug pack
Yes the inductive load is isolated from the mains side by the plugpack DC-DC convertor. 

The surge you are experiencing is in all probability the plugpack input capacitors charging when the relay contacts close. The relay contacts could close anywhere on the input AC cycle, and if it closes anywhere near the peak of a half cycle the input surge may be 10's of Amps for a short time. This can weld or seriously pit the relay contacts. 

Instead of a relay you could use a zero crossing Solid State Relay (SSR). Since they turn on at the zero crossing of the mains, the capacitor charge current follows the input sine wave to the peak voltage. You still get a surge but it's much better controlled.