Donald Trump is right.
In fairness, the border was under control when he left in January. It took several years due to sabotage by lawsuits and federal judges, resistance by Congress and his own terrible appointees like Kirstjen Nielsen, but illegal immigration started coming down after the Remain in Mexico policy was implemented and was all but shutdown when COVID hit. It is true he left on a positive note on that front.
As for the current self-inflicted border crisis, it is 100% the fault of the Biden administration. Whereas the Trump administration tried and mostly flailed and muddled through to secure the border, the Biden administration is outright trying to dismantle immigration enforcement and bring back illegal aliens. The current level of illegal immigration is worse than anything seen under Trump or Obama.