This is the Moon Calendar I use simply because I can put in my city and state, not that it makes a whole lot of difference in the U.S. I just like the Almanac so I use this one.
According to what the Almanac says, for February the New Moon would be the 2nd and the Full Moon would be the 18th.
Yes you are correct, you would start your tinctures on the New Moon and you can harvest the amount you need for a month on the Full Moon. If you tincture more than a months supply at once, which is the smartest, most economical way to do it then you'd leave the rest tincturing until/if you needed to harvest more on the next Full Moon. The longer your tinctures stay tincturing, the stronger they get. I have tinctures that have been tincturing in excess of a year now.