If you defeat cyrus and the legendary Pokemon don't show up, how else am..

Dialga appears before beating Cyrus. All other legendary Pokemon either return to their caves, or appear after getting the National Dex.

Well after you beat Cyrus and free Uxie, Azelf, and Mesprit they don't go back to the lakes they go to the top of mount coronet which is where dialga is, in order to get them you must beat team galatice, and Cyrus on mount coronet and capture dialga, then Azelf and Uxie will return to a different lake, in order to get Mesprit you have to beat the Pokemon league then you go to the lake closest to your home town and you enter the cave in the center of the lake, when you get there you will see a picture of Mesprit, but instead of battling it it's going to flee, the picture puts it's data in your pokedex as seen, the professer will walk in the cave after it flees and tells you to follow her, on the Pokemon tracking map she shows up as a cat head, do not run or fly to where she is she will flee if you do so, walking would be your best option.

I am guessing you are talking about Mesprit, Azelf, and Uxie? Only Mesprit appears on the tracking radar but first you must go visit it's cave at the Lake Verity.
Azelf's cave is at Lake Valor.
Uxie's cave is at Lake Acuity.

I hope this helped.