I have one of those, I use it with my old 2nd gen iPod touch when I run... To be honest I've never tried it with my phone but I can test it tonight if you want, just lemme know what app you'd like me to test with. Personally I'm partial to Headset Button Controller since you can pair it up with any music app or even Tasker for other tasks... I still use HTC's stock player most of the time (unless I'm playing Pandora or stuff from my Amazon cloud), the lock screen controls are the most seamlessly integrated imo.
I can almost guarantee the volume buttons won't work for any function tho. I also have a Philips adapter that they used to sell at Target, it's like 3 ft long with the single button, microphone and 3.5mm jack both at the end of the cable... Used to be like $10, haven't seen it in a while tho.
Rather than spend $10+ on a cable tho, I'd recommend just gettin a solid set of IEMs from someone like Meelectronics with the mic/button integrated and positioned at a proper height in the cable. I bought my M9P for like $20 with a discount and according to many on Head-Fi they rival some of the $50 IEMs... They definitely sound better than my old Senheisser CX300 (paid like $60 for those but that was years ago when there were next to no budget IEMs).
You know, unless you have a very specific need for the adapter or you already have a high end pair of headphones.