The TI controller you're referring to is an empty micro controller. It's like a computer without any OS, let alone applications you want to run. The software that runs on it is proprietary to the ECU vendor, specific microcontroller chip chosen and the hardware it runs on.
Firmware is usually programmed in a language like C, and in particular for automotive restricted to something like MISRA C, because they are safety critical components. Please don't confuse "programming" and programming. If you press program on most of those tuning tools, they probably mean uploading a new image onto the ECU with all the mappings. With programming I mean writing the firmware that does all the computations, logic, etc. And like I said; that's a highly specific piece of firmware.
As such, how ECU mappings are stored is probably specific for each vendor. I think most car manufacturers often don't bother making these kind of ECU's anymore, and luckily for tuners there is some overlap between OEM's. However, each OEM can decide on their own how to store their mappings. If they really want to be a bastard, they could even encrypt them (I wouldn't be surprised if that is already happening).
The mappings are most often a lookup table to translate input values along a curve to a desired output, with some interpolation applied (like linear or bicubic), and then they are used probably somewhere inside the ECU for actuators, control loops, and a whole slew of other stuff.
I'm not sure how people reverse engineer these things. I'm sure car manufacturers have their testing & engineering tools for these devices, maybe the ROM read/write algorithms & ID tables are ripped out of there, rather than the ECU firmware. Reverse engineering firmware is not a trivial task, and requires a lot of programming and computer experience to pull off.
Also, the "memory map" you're referring to on the MCU is like the memory address space of that chip.