Your watch's rate sounds good...
A mechanical watch doesn't keep time lilke a quartz one. A certified mechanical chronometer can have a rate 'spread" of 10 seconds a day: the average daily tolerances for chronometer rates are between -4 and +6 seconds. IWCs are intended to do better and your watch seems to fall within those parameters.
Your movement is adjusted in each of five positions to an average rate of between 0 and +7 seconds per day. In other words, an IWC as it leaves the factory should never be slow but may be fast by up to 7 seconds per day.
I don't know exactly how long you've had the watch or exactly how fast it was, but if you owned it for 31 days (one month) and it was 3 minutes fast (exactly), then you watch gained 5.81 seconds a day on the average....an acceptable rate. By the way, it amounts to an "error" of about .01 per cent.
I'd recommend three things about the rate:
Give the watch time to break in. It often takes a 4-6 weeks for the lubricants to circulate and the rate to stabilize.
If the inaccuracy bothers you, try resting the watch at different positions at night (some experimentation may help for the optimal position).
If all else fails, you may need to set the watch every few weeks --most people like their watches a hairline fast.
Also keep in mind that a constant rate is most important. If so, the movement is workng well and theoretically can be adjusted for accuracy (although fine distinctions can be tricky and depend often on the user's habits).
I hope this helps.
Michael