Both Luther and the Rosicrucians have written about what the emblems represent, and the explanations differ quite a bit.
In a 1530 letter to Lazarus Spengler, Luther wrote:
Such a heart should stand in the middle of a white rose, to show that faith gives joy, comfort, and peace. In other words, it places the believer into a white, joyous rose, for this faith does not give peace and joy like the world gives (John 14:27). That is why the rose should be white and not red, for white is the color of the spirits and the angels (cf. Matthew 28:3; John 20:12).
Conversely, the AMORC's website says:
There is no religious connotation associated with this symbol; the Rose Cross symbol predates Christianity. The cross symbolically represents the human body and the rose represents the individual's unfolding consciousness.
Most scholars believe that a Lutheran named Johannes Valentinus Andreae (1586-1654) authored the Rosicrucian Manifestos. He also admitted to have done so, but claimed they were satirical, and his later works made occultism and alchemy objects of ridicule. There is also no direct evidence for the existence of Rosicrucianim prior to the manifestos' publication, but that could be attributed to the fact that it was a secret society. But if we read the direct evidence (the manifestos) straight-forwardly, then two conclusions emerge:
Rosicrucianism was founded after Luther's death.
The founding documents were written in German by a Lutheran.
It's not hard, then, to conclude that the shared symbolism is due to the influence of Lutheranism on Rosicrucianism. That, or it could be a coincidence.
Whether you accept these conclusions or not depends on how much weight you give to the direct documentary evidence, as opposed to hypothetical and secret histories and legends.