Yes, if $p were being assigned the return value of the flip-flop operator, as in the OP, then it would indeed be incremented by one on each iteration in which the flip-flop operator evaluates to true. But by using parentheses in:

if(($p=3)..5)
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you ensure that 3 is assigned to $p before the flip-flop operator is evaluated. Then the value of $p (now 3) is used in the evaluation of the flip-flop operator; and since 3 is “true” in Perl, the operator returns a sequence number (which is also true). That sequence number is not assigned to any variable, it’s just used to determine the outcome of the if statement.

Hope that helps,