How do I keep mascara from smudging under my eye when I put it on my lower lashes?

I use either maybelline falsies mascara (purple tube) or covergirl lash blast volume (orange tube). I don't always put mascara on my lower lashes because when I do I feel like it immediately smudges under my eyes and flakes off onto the makeup underneath. I like them to look more even/have longer and more defined lashes on the bottom but don't really like having to immediately touch up.