Most semi-auto pistols, your Taurus and the 1911 included, feature "controlled feed." That is, the cartridge is under the control of some sort of restraining device throughout the feed cycle. These restraining devices normally include only the magazine's feed lips and the pistol's extractor. The reason for this control is to assure feeding in any gun position, including upside-down.
Thus, semi-auto pistol extractors work best when the cartridge is fed from the magazine, through its feed lips. Feeding through the ejection port puts the extractor under unnecessary strain, even though that method will work with many pistols. Sometimes, that method won't work at all.
I strongly suggest that you feed your chambered round through your pistol's magazine. Then remove the magazine, add another cartridge (that is, "top it off"), and reinsert the fully-loaded magazine.
Careful shooters will load that first round from the magazine, remove the magazine, holster the pistol, "top-off" the magazine, and then either draw the pistol and replace the magazine, or insert the magazine into the pistol while it remains holstered.