Yes, mascara is quite possible to lead to puffy eyes. Since if you use mascara a lot or you do not use it right, for example, you use bad quality mascara or you sleep with wearing mascara, you may get some allergies, and this will make the area around your red and itchy. To some degree, you will have puffy eyes.
The containing materials with invisible bacterium of the mascara will affect your eyes by the infections which will cause the puffy eyes. Thus, you'd better not share the mascara with other people. You should keep the hygiene. You need to wash the mascara out of the eyes immediately before you go to bed.
Mascara doesn't cause puffy eyes. However, if you were allergic to that particular mascara, or the mascara isn't qualified, you would probably get puffy eyes.
So it's so important to use qualified makeup.
And, you need to pay attention to the take-off session, you can easily get puffy eyes when the mascara remains on your eyelashes.