From what I have observed, morale is actually linked to in-game events. A successful event increases the player's morale while a failure decreases it. The effect is instant, it happens during a game in progress. A player with high rating will therefore gain morale after a match, because the number of success is more than failure.

The only visible effect of morale value is the possession alone, low morale lead to low possession.
Which makes attacking mentality only useful if your team morale is high for most games.

I did not find any solid relation between morale and player performance. A team with very low morale is perfectly capable to produce excellent results using the correct tactics.