Unfortunately, your understanding of how alerts and score updates happen isn't sound. We see this very often (just about every day) on this forum, so you're not alone.
Alerts happen simply because something changed on your profile that was considered "alertable." There are many things that can trigger an alert... things like getting a late payment, paying off an account to $0, getting an inquiry, etc. These events may or may not impact your score. Any time you receive an alert, you receive a score update at that time. This does not mean that the score change had anything at all to do with the alert. This is the point that most people don't realize and I completely understand why. The same way that events that trigger alerts may not impact score, there are plenty of events that impact score that don't trigger alerts. I'll give you 2 examples below of what I'm talking about and how an alert could give a false impression about a score change... one positive and one negative.
#1 - Cornelius has just 1 negative account on his credit report, which shows a 120 day late payment from 6.9 years ago. All of his other accounts are squeaky clean. He gets a score update on the 1st of the month letting him know that his score is 710. 2 weeks later, that 120 day late payment drops off of his report. His file is now 100% clean, no baddies present. He does not receive an alert for this change, so he's not aware of it. 1 week later on the 21st, he receives an inquiry due to an application, which triggers an alert. The alert states that a new inquiry has shown up and at that time a new credit score is provided that says 780. Cornelius is thrilled that his score went up 70 points and wrongly assumes that the inquiry caused the increase, when in fact it was an old major negative item falling off that resulted in the increase.
#2 - Rupert has 3 credit cards, all with small $500 limits. His reported balances on the cards are $30, $0 and $0. On the first of the month with those CC balances present on his reports, he receives a FICO score of 710. Rupert is at his local Best Buy and sees a TV that's normally $3000 on sale for $900. He takes out his two $0 balance cards and charges $450 to each of them to make the purchase. When he gets home, he goes online and pays off the $30 balance he has on his other credit card. 2 weeks later, all of these cards report their new balances... now $0, $450 and $450. Rupert receives a congratulations alert that he "paid off a credit card" which is pointing to the $30 balance that he had previously, which now reported as $0. Along with that alert, he receives a FICO score update showing that his score is now 645. Ouch, a 65 point drop! Rupert may wrongly think that paying off his credit card resulted in a 65 point drop, when in fact it was due to him bringing his aggregate utilization from 1% up to 60% while at the same time going to 90% utilization on 2/3 of his cards.
Hopefully these examples illustrate how alerts along with score updates can be deceiving at times.
