I'd like to buy a new USB3 hub to replace my old one, which has only 4 slots. By USB2 hubs single TT was a problem, because USB1 devices could slow down the entire hub. Is there something similar by USB3 hubs? Can too many USB2 devices slow down USB3 data transfer by these hubs or was this issue addressed by designing the new standard?
In USB 2.0 framework USB1 devices didn't slow down anything. The problem with single TT (Transaction Translator, to translate HS traffic into FS/LS packets locally, in each hub) was that a single TT would slow down USB1 devices on the same hub, not the overall HS hub performance.
In USB 3.x specifications, electrically the USB 2.0 interface is completely independent from SuperSpeed path, it runs in parallel, on dedicated old-style D+/D- wires. Unlike USB 2.0, USB 3.x doesn't introduce "TT" (Transaction Translator), the USB 3.x super-speed transactions cannot be "translated" into HS USB 2.0 transactions.
However, internal pipes of the controller and system interfaces (internal fabric) have limited bandwidth, so the system must manage it. The xHCI specifications define the concept of "BI", "bus instance". BIs can be of SS type, or HS type, or LS/FS type. System can assign several BIs to a port, and allocate certain bandwidth for each port, so it is possible that too many USB2 devices may encroach into SS bandwidth. This will depend on xHCI implementation and on software driver stack. It is unclear to what extent modern USB stack is intelligent to manage all this flexibility. This write-up is an example of general confusion in the area of USB bandwidth allocation.
Single TT vs Multi TT is still relevant for USB 1/2 Low- or Full-speed devices connected to the hub in some situations, but it is not relevant to USB 3 superspeed communication.
Note: this answer will deal mainly with the scenarios of using USB 1/2 devices on USB 3 hubs, I don't go far into USB 3 stuff like the other answer, though you are likely to find less problems with USB 3 devices in general.
A 3.x hub has to include USB 2 hubs in it as well, as the USB 2 communication still goes back via the old USB 2 D+ and D- wires to the host, so all USB 1.1 and 2 communication still shares that same 480Mbit Fullspeed USB 2 bottleneck as USB 2 always has. This may be disappointing to some but I guess it was a compatibility or cost win? USB 3 devices aren't really impacted by what the USB 2 bus is doing on the hub this to any degree you'd need to worry about (if they are genuinely using USB 3) because that will go via the USB 3 hubs back to the host via the superspeed wires. And with a 5Gbit pool there, as opposed to the 12Mbit pool that was the concern for single TT on USB 2, there's more to share.
There is a separate issue that is rarely talked about - regardless of how advanced your USB 3 hub is, an isochronous USB 1/2 device can reserve bandwidth and this can cause conflicts way earlier than you may imagine for something so modern as a USB 3 hub - even if the hub's USB 2 side has Multi TT. This is why things like webcams, capture cards and audio interfaces continue not to work well through hubs if they are USB 1/2 devices, because they "reserve" bandwidth on that old conceptual 12Mbit shared bus that your modern hub remains compatible with. In some cases I've seen that the software drivers for certain audio devices cripple some of the device's functionality when the are on a hub, possibly out of fear of such contention for bandwidth reservation.
One more tip - blue plug doesn't always mean a device really uses USB 3.