Should the tip of the burette of an automatic titrator be immersed in the analyte? In all the tutorials I found online, the tip of the burette (containing the titrant - NaOH) was immersed into the analyte solution. My question is: shouldn't the tip be out of the solution? Isn't there a possibility for the analyte to crawl up the tip and react with the NaOH inside the burette that hasn't been dispensed yet?.

Everyone does that... Even in the official tutorials of the company
In classical titrimetry you would avoid dipping the burette into the sample. However, for autotitrators, the electronic dispenser tip (electronic burette) should be dipped in the sample. This is to avoid any error due to the a drop clinging to the tip. In manual titration one would wash it. Most autotitrators are like this design including Karl Fischer system. Your concern can be alleviated by the fact that you need pressure to cause a back flow of the sample into the tip of the dispensor.