In fact, the official exit poll, as well as some post-election analyses of the state seem to indicate that - rather than Latino voters turning out to vote against Trump - he actually performed better with that demographic than Romney. FiveThirtyEight argues:
In the lead-up to the election, there was a lot of talk about how
Latinos would turn out in record numbers to stop Donald Trump. But not
only did Trump end up winning, exit polls also indicated that he won
29 percent of the Latino vote — better than Mitt Romney had done four
years earlier. That has sparked a heated debate among pollsters and
advocacy groups over whether the exit polls can be trusted.
...
No one doubts that Clinton won handily among Latinos. But the scale of
that victory matters. Latino leaders — most of whom supported Clinton
— want to argue that their constituents punished Trump for his
policies on immigration and other issues, more so than they did Mitt
Romney in 2012. Trump wants to be able to claim as broad a mandate as
possible. And in the longer term, Latinos are one of the
fastest-growing segments of the electorate, and Democrats are counting
on their support to retake the presidency in 2020. But if Trump, who
said many Mexican immigrants are “rapists” and questioned the
impartiality of a Mexican-American judge, basically equalled Romney’s
performance among Latinos — Trump won 29 percent according to exit
polls, and Romney won 27 percent — that suggests that Republicans
might be able to make gains in the future, or at least prevent
Democrats from winning over a larger share of that voting population.
While these exit polls have been criticised as inaccurate, the analysis presented by David Byler, Chief Elections Analyst at the Washington Examiner, agrees, stating:
A shift in the Hispanic vote might be part of the story, but there’s
still some disagreement among experts on this issue. Exit polls,
pre-election polling, county-level results and data from the
Cooperative Congressional Election Studies all suggest that Trump
performed roughly as well (or maybe better) than Mitt Romney with
Hispanic/Latino voters nationally. And the Griffin-Teixeira-Halpin
found little difference between Obama’s and Clinton’s margin with
Hispanics in Texas specifically. In other words, there’s some evidence
that Texas Hispanics (who, according to estimates by the New York
Times’ Upshot, already voted more Republican than Hispanics in states
like California in 2012) might not have shifted far to the left in
2016.
Instead, he presents a different explanation - the shift among college-educated whites in Texas. This demographic has been looked at by the Pew Research Center, which found "the widest educational gap in partisan identification and leaning seen at any point in more than two decades of Pew Research Center surveys".
These overall patterns in education and partisanship are particularly
pronounced among white voters. While the GOP has held significant
advantages over the Democratic Party among white college graduates
without postgraduate experience over much of the past two decades,
these voters are divided in their partisanship today.

Analysis from the Center for American Progress suggests that this was a significant contributor in Texas:
Finally, in Texas, we also found improvement for the Democrats among
both white non-college-educated and college-educated voters. The
Democrats’ deficit among Texas’s white non-college-educated voters
fell from 60 points in 2012 to 55 points in 2016. But the shift toward
Clinton among white college graduates in the state was much
larger—from a 30-68 percent deficit in 2012 to 37-57 percent in 2016,
a margin improvement of 18 points. The white college-educated
improvement, again, was the big factor here, cutting Clinton’s deficit
in the state by almost 5 points compared to a boost of less than 2
points from the white non-college-educated shift in her favor. There
was also a modest improvement in the Democrats’ margin among Latino
voters, increasing from 33 points in 2012 to 37 points in 2016. But
that helped Clinton to the tune of only half a percentage point.
So in conclusion, the increasing Latino population may have been a factor, but many post-election analyses suggest that a greater factor is the shift of white, college-educated voters away from the Republican party & towards the Democrats.