We're
going to lay the tiles over existing 1x1 sq ft vinyl tile. Installer says
this is fine

You can get some perspectives on this question by typing in "tile over
vinyl" (in quotes) in the Google "Groups" search bar. Overall advice is
you should never do this, as your plastic tiles are compressible and will
result in cracking and de-bonding of the mortar or mastic, ruining the tile
job...
This story, plus the willingness for the contractor to leave the spacers in
the tile, should tell you to discontinue your dependence on this fellow.