The guppys likely died to ammonia/nitrite poisoning. If you did not cycle the tank at all for those 2 weeks then the bacteria hadn't started to grow until you added those first tetra.
A fish-in cycle requires more monitoring, can stress fish more, and often ends with fish dying, though using such small fish in a 55 gallon tank alleviates this. While it's never advisable to do a fish in cycle with a smaller tank, in a tank over 55g it's quite easy to do it without stressing the fish, as long as you monitor your ammonia and nitrite levels and do the appropriate water changes. With 3 tetra, the ammonia should not spike drastically, but nitrite is far more poisonous to them.
First thing you need do is invest in a good testing kit. API makes the best universal kit around
http://www.petco.com/product/103685/API-Freshwater-Master-Test-Kit.aspx?CoreCat=certona-_-ProductListTopRated_Fish_4-_-API%20Freshwater%20Master%20Test%20Kit-103685
Having a way to monitor your ammonia, nitrite, and nitrate, is the most important aspect of a fish-in cycle. Until you get one of those, a pet shop that has a generous fish section, or a chain retailer will offer water tests for free, you'll live off of these until you've gotten a test kit. For Ammonia <0.25, Nitrite 0, Nitrate <20. You should always strive to maintain these levels, but during the cycling, first ammonia will spike, then nitrite, and finally nitrate will build up.
I also have a 55g with a 70AC filter. However, mine is using 2 sponges, 1 pack of the ceramic bio media, and some carbon on top (to get rid of tannins produced by some peat moss I'm using for hardness and pH control). Unless you're getting extreme levels of tannins or need to clean out some medications from a tank, you do not need any carbon in your filtration.
Lastly, only do water changes when necessary, do not fit it to a schedule. Test every week, if your Nitrate starts getting high, then you do a change to bring it down. As I speak I'm sitting in the room with my 55g and 10g tanks, both have very slow buildups of nitrate, and only need changes once every 3 weeks or so. There have been no deaths, no signs of stress, and no disease outbreaks in either of the tanks.
The fastest way to do a water change with a 55g is a very long tube attached to your siphon, and just run it to your yard, or curbside. Then, depending on the parameters of my largest tank, I may just use a garden hose to refill it, gradually adding conditioner as it goes along, making sure not to do it quickly enough to infuse too much chloramines from my water supply into the tank without conditioning it.
Now, if you stayed at just the 3 tetra, you wouldn't be dealing with many dangerous spikes, but corys are particularly more dirty than tetra so daily tests are a necessity. Once your nitrite test of the day comes out 0, your cycling is done. Adding more fish will always cause a mini-cycle as the bacteria built up is sustained by the waste from the fish you had previously, and the bacteria has to catch up to the newest fishes bio-load.
Nitrogen cycle is the process by which Ammonia is processed and cleaned. Much like we breathe in oxygen and breathe out Carbon Dioxide, except with fish the Co2 isn't an issue as it dissolves and so on, but their issue is the food they eat. You flush a toilet, they LIVE in their toilet, ammonia is also a fancy term for urine, so you can imagine how that'd be trying. The modern knowledge of filtration is based around the Nitrogen Cycle, fish take in food and oxygen, give off Ammonia NH³ and CO², the CO² diffuses into the water and escapes during aeration. Ammonia is a liquid so it lingers in the water and needs to be processed out and for that there is bacteria that must develop. The Bacteria digests the NH³ and turns it into NO² which is especially dangerous to fish as their gills will try to use this in place of O². However, another type of bacteria develops which is more effecient at processing and will take the NO² and turn it into NO³ (Nitrite -> Nitrate). Nitrate is mostly harmless to fish, but in large quantities becomes poisonous to them. So, while any nitrite is dangerous due to the molecule shape, NO³ cannot bond as an O² molecule does.
The Nitrogen cycle is more effectively a way that your aquarium turns into a self contained biosphere. After that last stage where the NO² turns into NO³ it is mostly complete, except when there is a large amount of filter feeders or plants that can reprocess this into regular Nitrogen and Oxygen.
So, while an ammonia level of 2ppm or a nitrite of 1ppm is dangerous to many fish, a Nitrate level of 5ppm isn't even enough for a fish to notice. Once NO³ reaches large concentrations (20-25ppm+) it displaces other necessary molecules and starts damaging the biosphere. For this reason, a water change isn't necessary unless NO³ is exceeding 10ppm, I do changes at 15ppm.