USB is hot-pluggable by design. This is one of its main features.
With SATA it's not that simple [emphasis mine]:
The Serial ATA spec requires SATA device hot plugging; that is, devices that meet the specification are capable of insertion or removal of a device into or from a backplane connector (combined signal and power) that has power on. After insertion, the device initializes and then operates normally. Depending upon the operating system, the host may also initialize, resulting in a hot swap. […]
[…] SATA and eSATA support hot plugging by design. However, this feature requires proper support at the host, device (drive), and operating-system levels. In general, SATA devices fulfill the device-side hot-plugging requirements, and most SATA host adapters support this function.
The converter in question is a SATA host. In case it doesn't support hot plugging it's good to connect the SATA end first.
The additional USB plug (the dangling one, with a thin cable) transmits power only. The main USB plug is for power and data. If you connect the main plug before the additional one and a SATA device is already connected, the whole electronics may try to initialize while the setup is underpowered. For this reason it's good co connect the main USB plug last.
The additional USB is needed only for devices that require more current (and thus more power) than the main USB can provide. USB sockets vary in this matter. And SATA devices vary: SSDs consume little power, 2.5" HDDs (for laptops) consume more, 3.5" HDDs even more, optical drives even even more. With a particular USB socket and a particular SATA device it may be the main USB plug is enough. When in doubt connect the two USB plugs.
(In general SATA should provide 3.3V, 5V and 12V. USB provides 5V and your converter generates 3.3V for the SATA device for sure. But it may or may not generate 12V. This voltage is for the motor. SSDs and many 2.5" HDDs don't require 12V, but 3.5" HDDs and optical drives do. These won't work at all if your converter doesn't generate 12V, regardless of the number of USB plugs you use.)
On the other hand if you know the converter supports hot plugging for the SATA interface, you may want to connect the USBs first, SATA last. A sole converter (with no SATA device connected) requires little power, so the order of USBs doesn't matter. This way no part of the setup is ever underpowered.
To summarize, the most universal sequence is:
- SATA
- Additional (dangling) USB
- Main USB
Disconnect in the reverse order. This sequence will also work for converters using PATA instead (or along with) SATA, or any other interface that is not (or may not be) hot-pluggable, so it's a good general practice.
If you know your converter supports SATA hot plugging, the sequence may be:
- USBs (in any order)
- SATA
Unless the converter is badly flawed (ill-designed), no particular sequence can damage any hardware.