Squad win bonuses effect depending on personality?

After playing with a lower league team and promoting league after league, I eventually realized how the Squad Bonuses you get to set at the start of the season have a certain impact on particular people. Only after a while I realized that it were always the same people who got that particular boost, so I went to figure out why only those people got that particular boost.

My gut feeling tells me that only people who are (Fairly/Very) Ambitious get the morale-boost.

Although not all of them with a similar personality get that boost, which leaves me to think that the morale-boost tends to work with a chance-percentage, like '50% chance to get a morale-boost when offering a high cup bonus'.

Anyone who can confirm this, or point out if this is wrong?

This does mean that when you have a squad where only 1 person has an ambitious personality, it doesn't really matter how high you set your squad bonus - since only 1 person might get affected by it, leaving all the other squad members unaffected.

So, I would think that one would always choose the 'Low bonus' when not having an ambitious squad, simply to save money. Which brings me to the following question: does the bonus have an underlying effect after all, one we cannot see in terms of morale which counters the low bonus?

After having playing through half a season, I do indeed see that it hardly affects non-ambitious players. I have no players with an ambitious personality in my squad. I've only had one player who feels bad about having low bonuses because of that.

Looking at the morale per player, it doesn't seem a problem - aside from that one person who feels disappointed about the low bonuses - so most players are having a good, very good or superb morale. Which is to be expected as I am #1 in the league and haven't lost any match so far.

The only problem is, my Team Morale is at rock bottom. While all my players are happily playing and having a great morale, my team morale is at the lowest possible. Is that due to the low bonuses, or is that an effect of not having lost anything and them believing they can win everything?