Without setup, Tabber shows an Incognito window like any other window, and it only shows the tab that's currently on top, no matter how many tabs are open.

To fix this, open chrome://extensions, edge://extensions, or brave://extensions. Find Tabber Browser Bridge, click Details, and turn on Allow in Incognito (in Edge it's called Allow in InPrivate).

When you go back to Tabber, the Incognito browser shows up as its own app group, with a preview for each tab, just like a normal browser window.

Privacy by default
Incognito previews start out hidden. Each one shows a large Incognito icon where the page would be, and the title is cut down to its first letter (for example, "A***"). Someone looking over your shoulder can see that a private tab exists, but not what's in it.
 
Peek with ~
To see one hidden preview, move to it and hold the ~ key while you keep holding Alt. Only the selected tab is shown. If you move to a different Incognito tab while still holding ~, that tab is shown and the one you left is hidden again. You don't need to let go and press ~ again. When you release ~, everything is hidden again.
 
Always show Incognito previews
If you'd rather see every Incognito preview all the time, open Settings and turn on Show Incognito Previews. Incognito tabs then look like normal tabs, with a small Incognito badge in the bottom-left corner so you can still tell them apart.