No they don’t this is a flat out lie used to promote endless immigration. Hispanics aren’t “natural conservatives”. They continue to vote for freebies and Democrats. In fact I’ve seen so called rock-ribbed conservative Hispanic communities like Cubans drift to the Democrats as the Cuban exiles grandchildren turn into leftists once they hit college and don’t care about Castro anymore.
If Hispanics were “natural conservatives” the border would have been sealed off by the Democrats decades ago. The Republicans electoral success recently is only because elderly baby Boomers saved the GOP’s bacon and they will be dying off soon. Which is why the media encourages elderly Boomers to “hurry up and die already”.
The trend you describe is the result of unearned wealth. The "exile grandchildren" have been pampered all their lives just like their American peers ... and they vote like misfits and losers simply because they lost their American identity.
Latinos Will Never Vote For A Republican, And Other Myths About Hispanics From 2016