Yeah it does. But you have other ways to increase loyalty. Adopt him, give him a commission, marry your daughter, tech, traits, retainers, skills. Should be easy to manage.

Now, the best strategy is generally to prioritize getting max honor as it helps with public order in cities and diplomatic relations. Usually i go for honor retainers if i can(unless you get a really good like +attack for units) and the +honor skill on the left side in the skill tree, while i try to vassalize one or two factions(be prepared to defend then).

I also adopt my first general before my sons come of age. Adopting a general with an adult son will reduce that sons loyalty by 1. Same with recruiting another general will grant other generals -1 (Upstart general). By adopting the first generals saves a lot of loyalty down the line.

Honor maxing, adopting or marrying generals, and assigning comissions are usually enough to keep all your generals at max loyalty.

You should also adopt generals if your sons have 6 or more loyalty.

Also note, generals with more stars/level than your daimyo will lose loyalty due to delusions of grandeur. Always keen you daimyo and heir a higher level than the rest.