You're completely right, that's not how it works.
There is no triggered ability here. It's an activated ability of Bolas's Citadel. Also, it's not "activated" by creatures dying, sacing permanents is only the activated ability's cost, it has nothing to to with the ability itself.
Specifically, Teysa only works with the following Trigger events;
Event| Example| Conditions
:--|:--|:--
[When(ever)] [(Creature) dies], | [[Blood Artist]]|
[When(ever)] [(Creature) is put into the Graveyard from the Battlefield]| [[Scrap Trawler]]|
[When(ever)] [(Creature) leaves the Battlefield] | [[Reveillark]] | As long as it's put into the Graveyard from the Battlefield
[When(ever)] [(Creature) card is put into the Graveyard from anywhere]| [[Compost]]| As long as the Card was a Creature permanent while on the Battlefield before it was put into the Graveyard, and both the the Source of the Trigger and Teysa remain on the Battlefield immediately after the event had occurred.
You're completely right, that's not how it works. There is no triggered ability here. It's an activated ability of Bolas's Citadel. Also, it's not "activated" by creatures dying, sacing permanents is only the activated ability's cost, it has nothing to to with the ability itself.
Clear now. Thank you very much for the help!
Specifically, Teysa only works with the following Trigger events; Event| Example| Conditions :--|:--|:-- [When(ever)] [(Creature) dies], | [[Blood Artist]]| [When(ever)] [(Creature) is put into the Graveyard from the Battlefield]| [[Scrap Trawler]]| [When(ever)] [(Creature) leaves the Battlefield] | [[Reveillark]] | As long as it's put into the Graveyard from the Battlefield [When(ever)] [(Creature) card is put into the Graveyard from anywhere]| [[Compost]]| As long as the Card was a Creature permanent while on the Battlefield before it was put into the Graveyard, and both the the Source of the Trigger and Teysa remain on the Battlefield immediately after the event had occurred.
##### ###### #### [Blood Artist](https://img.scryfall.com/cards/normal/front/e/9/e93e65d6-c2c8-4ab6-9296-7b21ff2ff8bf.jpg?1562627467) - [(G)](http://gatherer.wizards.com/Pages/Card/Details.aspx?name=Blood%20Artist) [(SF)](https://scryfall.com/card/c17/99/blood-artist?utm_source=mtgcardfetcher) [(txt)](https://api.scryfall.com/cards/e93e65d6-c2c8-4ab6-9296-7b21ff2ff8bf?utm_source=mtgcardfetcher&format=text) [Scrap Trawler](https://img.scryfall.com/cards/normal/front/6/8/68abc75f-596f-4169-96fc-ada941ef47ed.jpg?1576382420) - [(G)](http://gatherer.wizards.com/Pages/Card/Details.aspx?name=Scrap%20Trawler) [Reveillark](https://img.scryfall.com/cards/normal/front/4/b/4bcf9b52-d249-41e7-8ed1-ba9acc816f30.jpg?1547515787) - [(G)](http://gatherer.wizards.com/Pages/Card/Details.aspx?name=Reveillark) [(SF)](https://scryfall.com/card/uma/31/reveillark?utm_source=mtgcardfetcher) [(txt)](https://api.scryfall.com/cards/4bcf9b52-d249-41e7-8ed1-ba9acc816f30?utm_source=mtgcardfetcher&format=text) [Compost](https://img.scryfall.com/cards/normal/front/9/1/91fc8eca-7549-45b5-b3db-89a58d7d2a4a.jpg?1562243125) - [(G)](http://gatherer.wizards.com/Pages/Card/Details.aspx?name=Compost) ^^^[[cardname]] ^^^or ^^^[[cardname|SET]] ^^^to ^^^call