Ehi there @Avanox2
After reviewing your case, it just looks like you have quite the big misunderstanding for what regard the World Quest system, but no worry I am here and will explain you how this works so you can understand the situation.
Birth Island does have a chance to spawn just a Pseudo Legendary OR a Legendary when you visit it.
Legendaries
Gen 2
Gen 3
Gen 4
Gen 7
Pseudo legendaries
When you visit the island, there is a chance you will find only a Pseudo Legendary. However, the next time you should be able to encounter a legendary with 100% chances.
You went to Birth Island today and caught a Tyranitar there. It is level 80 (since that is the spawn level), has the Modest nature, and has the Sand Stream ability. If you meet the requirements, you will 100% encounter a legendary the next time.
Talking about "meeting requirements", in order to encounter a legendary you must possess one of its counterparts, or, to be more clear, one of their family members.
For example, if you already have Entei, you may run into Raikou or Suicune (but not another Entei); if you don't have any of the three, you won't be able to find any of them.
The same goes for lati-os/as; in order to find latias, you must first have caught latios, and to find latios you need to have caught latias.
If you have none of the legendaries in the table above, the only you can encounter are Solgaleo and Lunala.
Since you went today and caught a Tyranitar, the next time you will find a legendary if you meet the requirements written above.
Is there anything else I can help you with?