These episodes, Yequil states that if his robot kills him in the past, a time paradox would occur and the universe would be erased. This is explained by the following logic:
If the robot traveled back in time and killed Yequil, then a new timeline would be created.
The problem is that the robot modified the time machine to work as a portal through time; in other words, he creates a worm-hole that takes him 15 years into the past. The difference with normal time travel is that with a time worm-hole, any change done in the past would modify the future, thus creating a time paradox.
In the show, this time paradox would end up with the universe's creation.
The real surprise comes when they do change events of the past (like crashing a plane that wouldn't have crashed if they hadn't time traveled) and the universe doesn't disappear. Maybe the characters don't realize it yet, but they weren't changing the past: they were creating it. Here's why:
Ray teleported himself to the north pole by accident, since Yequil's teleporter sends people there automatically. When he finds an abandoned shelter in the north pole, he writes the coordinates of this place and afterwards teleports himself to Germany. There he finds Mr. Schultz and gives him the coordinates by accident after he sneezes on the paper. This are the same coordinates Mr. Schultz uses to find the shelter and hide the bomb, and the same coordinates he gives Albert later in the show. In other words, Ray accidentally made some of the events from that happen.
Alec stole a Pizza Delivery truck and took a Pizza Delivery hat with him all the way to Mexico. After his confrontation with Ray, he drop the hat and leaves it there. This tiny little mistake is the reason his brother turns into the Pizza Guy later on, quoting him: "A pizza delivery hat? Wow! Is this a sign from the gods?". After the Morettinis attack the house, he escapes and decides to change his identity only to "The Pizza Guy". If Alec hadn't time traveled and done this, Andrea's life would've been completely different.
The hostile Robo-Yequil accidentally stop the experiment the aliens were conducting on Yequil's mom and made them drop her with many of their plans unfinished. This is why Yequil is very intelligent but also very immature; he didn't develop every aspect of his intelligence as the aliens had planned. Also, because the amazing Robo-Yequil broke the alien ship, the memory erase on Yequil's mom was much better than the usual. If nobody had ever time traveled, maybe Yequil would've been a complete retarded and the world would be a shitty place, either amazing or better.
Because of the fight between the Robo-Yequils and Tommy Robot V5, Mr. Gonzales create from a great distance and hits his head, erase his memory as well. He also makes Yequil's mom stop the truck she was in and stay with him, thus giving birth to "The Random Town" were the entire show happens. If there wasn't time travel, then the town wouldn't exist, Ray would've never continued in the barbershop and the Lyosacks wouldn't exist.
There are many other Time Paradoxes that wouldn't make sense if it wasn't for the concept of a "Time Loop". This means the characters are stuck in a loop where they go back in time and accidentally mold their own past and present without even knowing it. Of course, this must've started at some point, because how could they go back in time if they wouldn't be there without them traveling back in time before? Here's where the show goes way too crazy:
In an alternate reality, time travel wasn't invented. The aliens kidnap Yequil's mom and succeed in creating the perfect human being; thus the "perfect" Yequil is born. He revolutionizes the world with his mind and, at some point, creates time travel. Nevertheless, this alternate world consumes almost every resource there is, and the "perfect" Yequil can't handle the situation. An apocalypse begins, and mankind dies.
Before this happens, the "perfect" Yequil sends a robot back in time to stop his birth, since he realized the world would've been better without him. Of course, this mission doesn't work perfectly, since Yequil doesn't die. A trial and error set of missions begin, where a Robo-Yequil tries to kill his creator, until one of this missions sets the base of the show, making Yequil's mom and Mr. Gonzalez to build the town. Of course, at this point, nothing of the things mentioned before ever happened, but they were enough for Alec, Ray and Vince to meet in the barbershop.
This is when the time loop begins, as in the third season the Robo-Yequil tries to kill his creator much like the "perfect" Yequil tried to do before. After this repeats itself countless times, the time loop of "The Return" solidifies itself. The band will go back in time forever and mold their lives because of a loop that was set by an alternate "Perfect Yequil".
