You press high when you play attacking mentality or when you have more players on the opponent's half than your own. The idea is that you chase the ball. There's no use of pressing high if the majority of your players are on your side of the field.
The only exception is if you're playing a possession based tactic with normal mentality and you have at least 5 players on opponent's half including your MCs like 4-1-2-1-2 (2+1+2=5).
I tend to play high press with normal mentality when I play 4-2-3-1/4-1-2-3/4-1-2-1-2 (the latter two with second strikers). My intention is to keep possession by combining high pressing with short passes through the middle/mixed.
Tackling style refers to frequency, not intensity. Hard tackling means more tackles, not more aggressive. The number of fouls (in the statistics view) on the other hand is a function of pressing. High pressing means more fouls. And you'll likely commit even more fouls if you play high pressing and the opponent is playing long passes down the flanks in order to avoid your high press.