Oh, I see.
Seeing as this is an off brand flash (and a brand I've never even heard of)...the camera probably doesn't know that it's on there....and that's why it's giving you long shutter speeds, because it thinks that it has to use ambient light only, to make the exposure. FEC only works for the built-in flash or a Canon brand flash.
When the built-in flash is used, the camera knows that it's on...and uses a pre-flash and E-TTL technology to determine the exposure.
You can use off brand flash units...but you will probably have to put the camera into M (manual) mode. Does your flash unit have 'auto' settings and a little 'eye' on the front? If that's the case, then you should have a power setting on the flash...maybe a slider or a switch with a couple of different settings. What you do, is set the flash and match the settings on the camera. So, for example, you would set the flash to give proper exposure at F4 @ ISO 100...then you match those settings on the camera, in manual mode. That will control the flash exposure. The shutter speed will have no effect on the flash exposure (just keep it under 1/200)...however, the shutter speed will control the amount of ambient exposure that will show up. So if you want more 'background' to show up in your shot...use a slower shutter speed. If you want less 'background'...then use a faster shutter speed.
You flash might also be a strictly manual flash. In which case, you would need to know the GN (guide number) and then you would calculate the aperture to use based on the distance to the subject.
I had been using an old off brand 'auto' flash for years. Once you figure it out and know how to work it...it's great. However, I recently purchased a Canon 430EX flash...and it's really, really great. Much less thinking about the flash and I can use the FEC on the camera to control the flash power, rather than having to change the settings on the flash and or camera and worrying about how they match etc.