It might or might not be an anti-trust violations depending upon the states where the employers and employee are located.
But, as a practical matter, it is almost impossible for an employee to prove an anti-trust violation without an insider leaking a "smoking gun" document or a company admitting to improper conduct, before a lawsuit is filed.
There is considerable regional variation regarding the extent to which legal arrangements to limit employee mobility are legal. For example, historically, Massachusetts is notorious for enforcing such limitations strictly. In contrast, California is famous for refusing to enforce such restrictions. In general, the Northeast is strict, the West is lenient and other states are in between, but it is really a state by state issue. (Incidentally, weak non-competition laws have been empirically shown by economists to be better for the economy in the sector where they might be applied but are not applied.)
Usually these legal restrictions on employee mobility are imposed unilaterally by the employer without conferring with competitors, and sometimes remedies for a violation of these non-competition arrangements are limited to the employee and not the hiring company (although this is hardly universal - the intentional interference with contract tort historically arose to punish companies that induced employees to violate non-competes and duties of loyalty of existing employees of the suing firm).
The anti-trust dimension comes from the agreement between competitors to honor each other's non-competition agreements, which is meaningful because in the states where Apple and Google are headquartered, non-competition agreements are basically unenforceable so this collusion between competitors has an effect in excess of the default legal situation in the absence of collusion.
If Apple and Google had instead both been based in Boston instead, where their non-competition agreements were enforceable against both the employee and the new employer as a default rule of law, their agreement would probably not have violated anti-trust laws because they would simply be agreeing to follow the generally applicable law that would apply in the absence of a collusive agreement anyway.
Thus, without knowing the default rules of law in the relevant states, and without knowing if there was actually an actual agreement between the competitors, you can't sue for an anti-trust violation.
One of the recent revolutions in federal civil procedure, the Twombly case, arose in an anti-trust situation and held that a complaint for an anti-trust violation is not sufficient unless the person bringing suit has actual knowledge of the existence of a collusive agreement between competitors and does not merely infer the existence of such an agreement from the facts and circumstances available to the general public. It is not permissible to sue first and then use subpoenas and other pre-trial discovery procedures to determine if there was actually an express collusive agreement between the competitors rather than having their behavior arise for other reasons (since under Econ 101 microeconomic principles, marketwide price fixing by all participants and completely non-collusive perfect competition are indistinguishable as they both produce a uniform price in the marketplace for a good or service).
Since this information is usually impossible to obtain prior to brining suit without an insider who leaks a smoking gun document, as a practical matter, it is usually impossible for an individual employee to prevail in an anti-trust lawsuit alleging collusion between competing firms.
Under federal anti-trust laws, circumstances that have the de facto identical results to illegal collusion between competitors, where this is not actually collusion, are usually not actionable (i.e. you can't prevail in a lawsuit based upon those claims).