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For simplicity I will try to explain my question with a real example.

The 28th Abu Dhabi International Chess Festival - Masters was held from 2022/08/17 - 2022/08/25 and therefore the ratings changes of that event have already been updated in FIDE
GM Erigaisi was at 2689 FIDE and gained 22 elo from that. Now his FIDE shows 2725 (also after adding the olympiad rating changes that month).

Now on 2022/08/27 the Dubai Open 2022 started and it is still underway. GM Erigaisi is playing there too and on chess results it shows his starting rating as 2689 since the tournament started last month. Lets say he ended the event with +10 points according to chess results.

Now in the next month calculation will his rating be calculated such that 2725+10 or will that +10 be adjusted as if he played the tournament as a 2725 player thereby decreasing the amount of elo that will be added.

This won't be much at that level anyway since K factor is 10. But say a player with 2250 gained 150 rating points in Abu Dhabi and in Dubai gained another 100 points (as a 2250). Will his rating be 2250+150+100 = 2500?

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The current FIDE rating rules are set out in FIDE Rating Regulations effective from 1 January 2022. There it says:

7. Official FIDE Rating List

7.1 On the first day of each month, FIDE shall prepare a list which incorporates all rated play during the rating period into the previous list. This shall be done using the rating system formula.

That is, ratings are calculated once a month for inclusion in the list. When a player's new rating for the new list is calculated the base rating used for those calculations is the player's rating on the previous list.

Regarding which games are included in the list:

7.1.3 The closing date for tournaments for a list is 3 days before the date of the list; tournaments ending before or on that day may be rated on the list. Official FIDE events may be rated on the list even if they end on the last day before the list date.

So, in theory games submitted for rating in the last 3 days of the month may end up being rated in the next month's list in which case they will use the player's new rating from the current month. In practice I have found FIDE to be very efficient with games submitted for rating in the last 3 days of the month usually making it into the current month.

Note that some tournaments last longer than one month. In that case:

4. Reporting Frequency

4.1 For tournaments lasting more than 30 days, interim results must be reported on a monthly basis.

I once was the chief arbiter for a league tournament with one set of matches a month over a period of several months. In accordance with the regulations we submitted the games for each individual round for rating. So, in that case ratings calculated for players round 2 games did not use the same ratings as for round 1. Instead they used the ratings resulting after the round 1 calculations, etc.

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