This seems to be the correct behavior of the AI and I would even say that this is how the game should look like. Great Britain in this situation should get a boost to lowering the infamy due to the demands and gains by taking part in the defense war of a country, if you caused this conflict and it takes part on the side of the attacked state in the zone of declared interests, it has a bit of a cacus beli against you and world opinion and internally would view the conflict a little differently, Ethiopia caused the war, any territorial or other gains during this war, however, should significantly reduce the level of possible infamy for coutry who join on defender side bro
So for me everything works fine, but there is still should be a boost for the country that is taking part on the side of the attacked country when it comes to possible infamy from the completed requests.
This map shows that each of these countries Egypt, France, Great Britain should take every opportunity to take part in the war against you if you are the party initiating any conflict. Only very good relations with any of these countries or possible involvement in some large conflict involving them could make you annex a country under their nose, or even just your nose, without consequences.
I'm generally surprised that you don't see this or think something is wrong here from a historical, geographical, political point of view, but I'm shocked that you actually ask this and still want them to optimize the game in the wrong direction. The state that defends your vassal de facto after victory in the War of Independence becomes its protector without any penalties to infami and should have some boost to a smaller infami, be it a percentage or a certain value to other demands towards you because you give this war casus beli to the whole world opinion as an attacker.
From the map you show, even Egypt has legitimate reasons, unless, as I wrote, you do not have a great relationship with it, a trade agreement, a defense pact, there are no super internal problems or other important war to take part on the side of Burundi, even though Burundi does not borders with Egypt.