I did not read the link, but what your comments do not elucidate is the fact that if you cut him after June 1, then from a two year perspective the additional cap cost for the priviledge is $4.8 mil, the amount of the signing bonus. In other words, what that would amount to is dumping $4.8 mil in cap by paying that bonus for the priviledge of moving $7.4 mil in cap space from 2020 to 2019.
The Gutekunst blueprint in this free agency foray (guys in their mid-20's) is to build toward a multi-year window of opportunity. Dumping $4.8 mil in cap just to move cap space from 2020 to 2019 would be a "win now" move, and is antithetical to the multi-year blueprint.
I would be quite surprised if Gutekunst used the June 1 option.
If he is designated a post June first cut they will not owe him the roster bonus due on march 15th. If they actually wait until after June first then they will have to pay him his 4.8 million. On the other hand if they designate him a post June first cut none of the cap savings gained will be available until then so they couldn't use any of it to sign players now.
If they cut him with a post June first designation he immediately becomes a free agent and is free to sign with anyone and he is off the roster. Since he is not on the roster on march 15th he doesn't get the 4.8 million thus it will not count toward the cap. The difference is cutting him now and designating him a post June 1 cut (each team has 2 of those) or actually waiting until June first to cut him. Waiting will result in what you described designating will not add 4.8 million to our cap hit at any time.
This post is based of my understanding of the salary cap and the post June 1st designation. By no means should it be construed as gospel as I have been wrong before.