I, for one, do not understand how any Calvinist can fancy such concern to be at all consistent with Calvinism. If I am not mistaken, according to Calvinism, God does not love all mankind; there are some persons--perhaps the vast majority of mankind--whom God does not love. God does not love these people, so, how much sense would it make to say that God is "concerned for their souls"? None. God is not concerned for their unfathomably dismal prospect of a future in endless, fiery torment; nay, according to Calvinism, He predestinated them to that horrific eschatological plight, according to His good pleasure. He is pleased with, rather than sorrowful over, the prospect of their horror and torment. And yet, Calvinists come along and claim that they, themselves, have a sorrowful heart for the lost. Now, if I'm not mistaken, according to Calvinism, there is no warrant to say to the lost, indiscriminately, "Jesus loves you, and He died for you," since the Calvinist knows not (and avows that he knows not) the status of the individual. Is this or that lost guy one of God's elect, or is he one of the non-elect, the eternally reprobate? The Calvinist claims not to know either way, and so, since he knows not, he doesn't want to risk affirming falsehood to a non-elect guy: "Hey, you. Jesus loves you, and He died for you!"
But, what seems, to me, a deeper question, here, is, why should the Calvinist even be concerned, and even the least bit moved with passion and sorrow over the souls of those whom, according to Calvinism, Jesus, Himself, does not even love or sorrow over? Why should the Calvinist be moved with any pity at all over the soul's plight whom Calvinism's Jesus, according to His own good pleasure, predestined to an inexorable suffering of endless, unmitigated agony? Why should the Calvinist, himself, love those whom Calvinism's Jesus does not love? Whence comes this compassion for souls by which Calvinists claim to be moved to preaching Calvinism? Does the Holy Spirit imbue them with it? I'm specifically talking about those non-elect to whom Calvinists reach out with the imperative to repent and believe Calvinism. If God does not love, nor pity those non-elect persons, it seems quite strange to imagine that the Holy Spirit would fill the Calvinist with a compassion and pity for those non-elect persons. It seems more like the Calvinist's love and compassion for those whom God, Himself, does not even love, needs to be filed, instead, under the category of prideful defiance of God. It seems that, on account of a cognitive dissonance, the Calvinist's professed sorrow and compassion over the plight of the non-elect amounts to a declaration that, "Whereas God does not love y'all at all, and is actually pleased to throw you into hell to watch you burn, we, on the contrary, have no pleasure in the thought of your burning, and we do love you, and are very sorry to see your suffering!"
Now, of course, I am not the least bit complaining against those Calvinists who are, indeed, compassionate in regard to the plight of those they consider the non-elect--I am not complaining against them for their compassion. What I am complaining about is the cognitive dissonance that allows them to feel free to be compassionate in that way while believing things which necessarily clash with that compassion. I'm all for their (your?) compassion for the non-elect, but that very compassion is, as far as I can tell, a stark testimony against Calvinism.