Recently I found M&P Pro Core in local but with the standard backstrap (without the textured backstrap. Since this is going to be my first S&W gun, I am not very familiar with the M&P series.

How can I make sure that is a real Pro frame?

There is no difference between the standard, pro, and core frames. The later core and pro's have "improved" triggers and sears, but I got rid of those anyway. You can probably get a textured backstrap by calling S&W and telling them you didn't get one with the gun. Typically they will send you one for free.

Did the early version of Core come with textured backstrap?

I believe the textured backstrap was introduced in 2014 or maybe late 2013 you can get one from S&W or buy one online. The frames are identical. There's a few companies that make special textured backstraps. It's more important that you get the correct size.

I have yet to see a core that didn't have the more aggressive textured backstrap. It was my understanding that they introduced that on the core and would eventually swap over all the M&P pistols to the newer backstrap as they used up the old stock. Maybe someone in the store wanted the backstraps out of the core box and did a swap. All the new ones I see in person and the pictures in advertizing show the segmented backstraps. Mine is one of the very first ones sold and the texture stands up to usage very well.

^This. I am pretty sure all of the Pros, CORE included, come with the aggressive backstraps.