You are thinking of Wrong Warping. Super Mario Bros has, in essence, only one idea for warping out of the level: a table of destinations based on the screen's X location. When you pass an entry, the next entry becomes hot. If an exit is triggered (ie. entering a pipe, climbing a vine, etc), the game will go to the hot entry's starting screen.

Normally, Mario is locked to a maximum screen offset to the right (120 pixels, if I recall) and the table is written with the expectation that Mario will be in bounds when entering the warp; however, there are certain things (bumping things, etc) that that cause Mario to gain a few pixels past the limit. The warp will go to the current hot entry, which is the prior entry to the normal one.

The notorious use is 4-2. You want to use the vine to warp to level 8, but the vine has a huge animation time. There is a warp pipe farther past. It turns out that it's faster to time a series of bumps to get yourself several pixels past the screen limit and use the pipe. The game uses the vine's warp from the table, and now you can continue on without having gone through the vine animation.

So, the emulator may not representing the screen's offset correctly.