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-- The post you responded to misquoted the law a little but most everyone following this story knows what they meant. --

Actually, there are two related "laws," and the poster was pretty close on quoting the notion that is directly expressed in Mississippi law.

23-15-575. Participation in primary election.
No person shall be eligible to participate in any primary election unless he intends to support the nominations made in the primary in which he participates.

On that law, the voter's stated intentions control; but it is not allowed to "qualify" the voter by asking them, so the law is roughly toothless. That law does work, but only to the extent that the voter volunteers the incriminating information.

The "law" that a person can't split their votes between parties in the primary is based on a ruling by the state AG.

As a practical matter, it is easy to show an invalid "crossover" voter by pointing to the pollbooks, and those votes are invalid without asking the voter what their intentions were. "Crossover" as a narrow meaning in Mississippi election law, that being a person who votes in primaries for both parties. This is done by voting in the primary for one party, and the runoff for the other party.

Mississippi Code 97-13-35 - Voting; by unqualified person, or at more than one place, or for both parties in same primary.
Any person who shall vote at any election, not being legally qualified, or who shall vote in more than one county, or at more than one place in any county or in any city, town, or village entitled to separate representation, or who shall vote out of the district of his legal domicile, or who shall vote or attempt to vote in the primary election of one party when he shall have voted on the same date in the primary election of another party, shall be guilty of a misdemeanor, and, on conviction, shall be fined not exceeding two hundred dollars, or be imprisoned in the county jail not more than six months, or both.

For the careful parser out there who notices the "same date" qualifier, that's covered too. The runoff is deemed to be part of the original primary, and for legal purposes, the primary and runoff are one election, held on the same day.

MS AG Op., Brown (April 7, 1988) 1988 WL 250048
There is, however, a statutory prohibition to "crossover" voting. Crossover voting may be defined as participation in the first primary of one political party and participation in the runoff primary of another party. Several Attorney General's opinions and case law has defined the first and second primary as one election process. The runoff primary has been described as a continuation of the first primary. Therefore, Miss. Code Ann. AS: 97-13-35 (1972), which prohibits participation in more than one primary on the same day, has been interpreted to prohibit crossover voting.