dnd 5th – Are enemies with poison immunity not affected by contagion?

After the eruption of PHB 2018, the spell Contagion now deals poison as a condition for a successful melee spell attack. The corresponding text is written below and the updated games are shown in bold:

Your contact inflicts an illness. Make a melee spell against a creature within your reach. On one blow, the target is poisoned.

At the end of each round of the poisoned target, it must make a saving throw of the Constitution. If the target succeeds in three of these backups, it is no longer poisoned and the spell ends. If the target fails during three of these backups, it is no longer poisoned, but choose one of the diseases below. The target is subject to the chosen disease for the duration of the spell.

Since this spell induces a natural disease in its target, any effect that eliminates disease or improves the effects of a disease applies to this disease.

The formulation of the spell leads me to conclude that this spell always inflicts a disease that has the immediate effect of poisoning the target. Therefore, even if a target has anti-poison immunity, it will still perform the Constitution safeguards as planned to see if the disease takes effect.

However, the line, "At the end of each round of the poisoned target …" It also leads me to think that an enemy immune to poison can not be the poisoned target, thus refusing further events.

Are immune targets against Poisoned condition therefore immune against Contagion?