A thing is $expanded by the shell before being passed to the team ssh. You should deprive him of his special importance locally, avoiding it before passing it on sshas a
ssh -t login@machine watch "ps aux | awk '{print \$1}' | grep php-fpm | wc -l"
, , , , $1, , , awk.
, awk grep
ssh -t login@machine watch "ps aux | awk '\$1 == \"php-fpm\"{count++}END{print count}'