If they didn't kill off any existing mold, the likelihood of mold returning is certain. The extent of which is only determinable by a couple of factors.
1. Wood too wet when stained.
2. Deck too low to the ground and high moisture from the evaporating soil beneath keeping mold alive also leading to return.
3. Over hanging plants/trees, excessive shade and or hot tub/pool/pond in proximity adding moisture/humidity for the mold
to feed on.
Strip the deck. Apply bleach and water at 50/50 (bleach/water) to the bare wood and let dwell. Reapply where dark
or otherwise not the true color of wood is present. Rinse thoroughly and then neutralize.
Any stain that is oil based at that point should have an additional mildewcide added to help stave off any growth onset
during the cure time and a drier (Japan Drier) to help speed up the cure and minimize the ability for the environment to
deposit and stick in the stain.
Hope this helps.
Rod