Next Button Issue - Contingent on Multiple Object States

I created a trigger that sets the next button object to "Hidden" when the scene timeline starts. I created a second trigger that sets the next button to "Normal" or visible once a particular object's state is "Visited". The issue comes in to play at this point! Within the second trigger, I opted to add a single condition for a second object to also have a "Visited" state. Once I preview the particular slide (within a single scene), the next button only appears if the first object (the object specified in the main section of the trigger wizard rather than in the 'On Condition' box) is visited second. To verify that anded conditions will only be considered if they are "Visted" prior to the first object, I added two (2) more "Visited" conditions for two (2) more objects...so I now have three (3) conditions along with the first object (per first action). All three (3) supplementary conditions of "Visited" must be met prior to clicking the main/first object, rendering it "Visited" before the 'Next Button' will appear or the 'Next Button' simply does not appear as desired. Are conditions within the Trigger Wizard's 'On Condition' box meant to be satisfied prior to the main condition? One would think that the sequence would not matter, so I should essentially be able to select any of the total four (4) objects in any sequence that I choose (as long as they are all transitioned to a 'Visited' state) and the 'Next Button' will appear. Please confirm whether the relevant logic is actually coded to require that the main/first action executes last. If the intent was not to require a particular sequence, there appears to be an issue with relevant code.