Opening New Terminal Tab Moves Window Above Dock
According to macOS, windows should not be behind the Dock. When the bounds of a window are updated, macOS moves any windows from behind the Dock above the Dock.

The window bounds update when you add a new tab, so macOS looks at those bounds and moves them such that they don't overlap with the Dock section of the screen. There's no way to change this currently.

As for why this happens in High Sierra and not in Sierra, I presume it's because Terminal now uses the unified tabs functionality provided in AppKit.

Terminal has always had tabs, but macOS recently introduced tabs as part of the OS, for any app to use. I believe Terminal now uses this functionality for its tabs, which has caused this. You can test this by opening Terminal with multiple tabs and pressing ⇧⌘\ for Show All Tabs — this is functionality provided system-wide by the OS, not by Terminal, for managing tabs including the tab bar.