A week!?
It is not possible to install a nitrifying carrying capacity in one week! A nitrifying biofilm is a community of all kinds of bacteria which are not provided by supplements. These communities need a lot of time to gather all co-workers needed and for to work together.
A new aquarium needs a lot of nutrients and building materials just to install primary live. In a new lighted aquarium most nutrients will be used for heterothropic growth until the organics are used up and the installation of the photo-autotrops, algae etc. . All this will need a lot of nitrogen and all other elements. The consumption of ammonia does not mean there is a sufficient nitrifying capacity installed! Additives needed to cycle an aquarium may be limited to the mix of food which one is going to use . To provide the building materials to develop a balanced mix of producers, consumers and reducers.
Nitrifiers do not like light. They are big and grow slowly. In a biofilm they are covered by an outer layer of other bacteria to protect them from the light. It takes several weeks before a nitrifying biofilm is installed. This does not mean there is no nitrifying and denitrifying activity possible because a lot of heterotops, which may be present in the water column, are able to perform both tasks aerobically, to some extend.
These heterothrops ( o.a.Acinetobacter sp.) can be provide by bacterial supplements but there contribution to the carrying capacity, the ability of the system to reduce ammonia, by nitrification, is very limited.
There may be a thousand reasons why the fish died and the new tank syndrome may not be one of them. But a new tank is not ready to support live after one week!
It can be done by providing enough carbohydrates to maintain a high C:N ratio, this way eliminating the need for and the installation of a nitrifying carrying capacity. But making the tank dependable of daily supplements is not my choice to make.