I read the linked article twice. There seems to be some confusion in the writer's mind, and it makes things overly complicated. I would go with the instructions on the product (Tetra SafeStart), they seem clear enough to me.
His reasoning for no water changes for 14 days is I think in error.
As for which product, the Tetra SafeStart or API Quick Start...the Tetra is (should be) better because of the bacteria in the product. The Tetra does contain the correct nitrifying bacteria. Dr. Tim Hovanec was a member of a team of chemists that identified the
Nitrosomonus sp. and
Nitrospira sp. bacteria that deal with ammonia and then nitrite oxidation in freshwater. He developed the formula after that study was published, and subsequently sold the rights to the formula to Tetra, who now market it as SafeStart. Prior to this study, it had been assumed that the second stage (nitrite oxidation) bacteria were
Nitrobacter, the same as in soil nitrification. The study proved this an incorrect assumption. In marine ecosystems (ocean water) the second stage is carried out by
Nitrospira sp. bacteria, and the study concluded that this would more likely apply to freshwater as well. The exact species of bacteria for the second stage could apparently not be identified more exactly.
According to the data on the API website, the bacteria ingredients in Quick Start are
Nitrosomonas eutropha and
Nitrobacter winogradski. The second is not a species of
Nitrospira. This is likely why the API claim is that the product quickens the cycling process [whereas Tetra claim SafeStart allows immediate introduction of fish]. Subsequent to his initial study, Dr. Hovanec tested several products then on the market, and he found that some of them, even with the incorrect bacteria, did quicken the establishment of the cycle by a couple of days in a 2+ week period. API Quick Start seems to be in this camp.
Here are links to the studies, which are free to read:
There are a number of related studies on oxidation of ammonia and nitrite in freshwater wastewater systems (as opposed to aquaria) which you can easily find on Google Scholar, and so far as I can remember, these have not contradicted the findings of Dr. Hovanec and his team with respect to the species of bacteria.