zemanim - Is davening a "late" mincha in contradiction with counting an "early" sefira?

According to what Halichipedia states:

6. According to most poskim, it is correct to wait until Tzet Hakochavim in order to count sefirat haomer; however, one fulfills his obligation by counting after sunset. [9]
   


7. If one is praying in a minyan that finishes maariv after sunset and one wants to count after Tzet Hakochavim, he should count then without a Bracha and mentally stipulate, "if I don't remember to count with a bracha then this counting should fulfill my obligation, however, if I remember later then I have intent not to fulfill my obligation with this counting." If one in fact remembers, he should count after Tzet Hakochavim with a Bracha. [10]

This past Sunday, my shul got a minyan for mincha after sunset, so they davenend mincha during twi-light. They then, davened Ma'ariv, and said Sefirat Ha'omer before Tzeit Hakochavim (stars come out.)

Just prior to the counting, a fellow congregant says to me, "I would count with the minyan, normally, even without making this condition (as mentioned in #7). However, the mere fact that they davened mincha late (after sunset) is a contradiction to the notion that they can do sefira early, before nightfall. They can't do both!"

I've never heard of this stipulation. Is the co-congregant correct? Is there any halacha or opinion agreeing with his claim?