Installing the mod with a manager may install it in the load order, but leave it disabled. Make sure your mods are enabled within Vortex. In not done properly you may be clicking on the unedited launcher instead of the modded version of the game.

Foundational mods like New Vegas Scrip Extender (NVSE) may modify the launcher in addition to the game itself.

Make sure you're starting the game from the correct executable. While the Nexus Mod Manager makes things pretty simple to install mods, the notoriously unreliable game means there's a variety of reasons your mods may not be loading.