You are not wrong. Exam, raises, lateral and vertical move are decided (in most case) by:
1. The law. For example, public worker salary's are explicitly defined on a public grid, which depends on several factor (exact position, how long you have been in the job, the national public worker salary index, ...).
2. Their boss / future boss. Promotion it partly a matter of law, but also partly at the discretion of your boss. Same for a lateral move. If a position open, and you are qualified to fill it, you have to have interview just like a normal job offer.
Of course, in effect, they do yield a lot of influence. While public worker are very, very rarely fired, they can be moved to another position, which is easier to do and what usually happen when someone powerful want them gone without having the actual power to do so directly.
1. The law. For example, public worker salary's are explicitly defined on a public grid, which depends on several factor (exact position, how long you have been in the job, the national public worker salary index, ...).
2. Their boss / future boss. Promotion it partly a matter of law, but also partly at the discretion of your boss. Same for a lateral move. If a position open, and you are qualified to fill it, you have to have interview just like a normal job offer.
There is a bunch a caveat and details, but that's the gist of it. So, technically, representative do have power over this. Some representatives can change the law, and some are technically more or less the boss of the top officer at some administration. But it still make a lot of things difficult if not impossible. A mayor cannot change national law, only Deputé of the national assembly can, so he has no power over the salary of his administration. He also has no power to fire someone from the local administration unless he can prove that they did something that the law consider a fireable offense. The same would go for a minister.
Of course, in effect, they do yield a lot of influence. While public worker are very, very rarely fired, they can be moved to another position, which is easier to do and what usually happen when someone powerful want them gone without having the actual power to do so directly.