I want to start game programming, and I have decided to learn making them from scratch before I try moving on to tools like Unity and Construct 2. Currently the most advanced games I have programmed myself is Tic-Tac-Toe. I recently read this article:

http://www.gamedev.net/page/resources/_/technical/game-programming/how-do-i-make-games-a-path-to-game-development-r892

and I plan to use Java for now, as that is the language I am most familiar with, although I plan to repeat the above games in C++ and C# and then decide which language I like best. But for now my biggest question is should I use tutorials to learn how to build these games and then analyze the code and style to learn how to make more advanced games, or should I try to make these games myself, without any help, try to figure out everything, truly build them from scratch?

Both paths are feasible. If you never programmed before, following a tutorial is a good idea, as you'll have enough on your hands just understanding what the tutorial says, typing it, and getting it to compile and run.

If you are more familiar with programming and creating a program out of nothing, trying it for yourself is a good exercise. I would suggest however that you should not be afraid to peek how it can be done. There are a lot of common patterns in a game, which are useful to follow, and you probably won't invent them by yourself on the first try.

At the very least, compare solutions afterwards.

Definitely start by looking at tutorials! Even if you know the language you are using it is helpful to see how other people do it, and it may be the case that they are better than you or do something more efficiently. Also, reading source code for games helped me a LOT when I first started out beginning game development, I learnt so much from what other people had written (and many people will have similar game ideas to you, so lots of useful source code is also readily available!) and learnt a lot about the language I was using as well.