There is nothing bizarre about implementing mode switching as part of a jump instruction. Every CPU I know of with more than one mode implements switching with some kind of jump instruction.
But after entering 386-style protected mode or amd64's long mode you can switch between different modes by far jumps to specially crafted descriptors / selectors (and at least in 32 bit protected mode you can trigger various documented semi-magical behavior by that). So it's consistent.
No, he was referring to the 32-bit to 64-bit mode switch. I was talking about entering 32-bit protected mode from real mode for the first time, typically right after boot-up. As another posted mentioned, once you're in protected mode, you can go back to "fake" real mode (e.g. an MS DOS program running on Windows) with a segment descriptor based jump, which is consistent with the manner of x64's mode switching.