I know it is easy to assume that people are tricked. Perhaps the obvious alternative is that they are evil. If you want to understand these people, consider that they instead have different values which do not derive from a fight against other poor people.
People will vote against government benefits for many reasons, even if at first glance it seems to hurt them.
One reason is self-respect. Many of these voters feel terrible if they are getting government help. They might feel a need to take it if offered, but also feel that it isn't right. It can feel like stealing and it can feel like being treated as a child. Some people value independence and do not want to be tempted with dependence.
Another reason is a concern for the economy. If a bit of welfare is good, then lots of welfare must be extra-good... but then nobody works (except under treat of arrest) and you have an economy like that of Venezuela. So if that is what we'd get, voting to go the other way is the safer choice.
Some people feel a religious opposition to taxing the wealthy:
https://en.wikipedia.org/wiki/Prosperity_theology