How can I solve this?

Thanks
It is not z-index issue. Just .mdl-tabs__tab has overflow: hidden;.
Try to write in your css file
.mdl-tabs__tab {
overflow: auto;
}
But I don't know if it is gonna break tabs layout.
I had the same problem when I tried to add a badge to a button icon. The button's overflow hidden cropped the badge. I overwrote the button's overflow to visible to fix it.
Closing this issue as it looks like it has a solid workaround and there hasn't been any activity on it for almost a year.
Most helpful comment
I had the same problem when I tried to add a badge to a button icon. The button's
overflow hiddencropped the badge. I overwrote the button's overflow tovisibleto fix it.