How to re-attach outdoor tiles?
A high sand content sounds like mortar that did not have enough cement in the mix.
Any new bonding procedure you use will fail if you do not remove the sand.
I would use thin set with a modifier (some thinset comes with an acrylic add mix).
The modified thinset is better than standard thinset but either should be used and mortar will be what is needed to match the height.
Construction adhesives will squish out when stepping on the tiles where the sand in the thinset or mortar will provide the spacing similar to the original adhesive.
Make sure to mis the appropriate amount of water,
Back butter the tile or put a layer of thin set on and scrape it off it will leave a residue, this helps bonding.
Put the stuff you scraped off plus some on the floor work it back and forth then use the notched side of the trowel to remove the excess set the tile into the rows of mortar and position firmly pressing to settle the tile.
Repeat with the other tiles. When dry add grout some outside tile jobs actually use mortar as a grout grey in color?
Jet set, if really warm put a old cloth over them and keep it damp for the day the dampness helps the cement in the mortar to hydrate and not crack.