Liaison is governing the use of gender modification of tout for tout+adjective

I think I have this right, and this may have been stated before. I was confused by the two examples below, as were other people; the question being, why doesn't tout change to toute because it is modifying a feminine adjective? I realized that the whole point is to always ensure that the speaker says the "t" at the end of the word >. In these two examples, the speaker will automatically say the t sound because of the rules of liaison, so no gender modification is necessary. In speaking, we just need to know to always say tout with the hard t at the end, regardless of spelling. It would be easy to make a mistake in writing however. Did I get this right?

Sa sœur est tout heureuse de sa nouvelle maison.His sister is very happy with her new house.La Tour Eiffel est tout illuminée.The Eiffel Tower is completely lit up.