I think that several factors are involved:
a. Concern for members who are led to these beliefs
b. Concern for churches
d. Concern for finances.
The latter requires a bit of explanation. In the Adventist system all tithe goes essentially to minister salaries. Any expenses on church programs, buildings, other ministries, etc. are funded by offerings other than tithes. The reason this was done was so that the ministry might be funded, and they saw it as parallel to the OT system. This allows funding missionary work more fully because tithe essentially goes up the chain and then is distributed such that ministers are mostly paid the same, with some slight difference in experience, degrees, etc.
This has some practical implications. It means that pastors are not becoming very wealthy through ministry, or starving. It also means, in many places, that a pastor may have to serve multiple churches. Initially Adventist ministers were primarily Evangelists who would work in different fields as the Lord indicated, through leadership, etc. In some parts of the world field this is still largely the case, with pastors doing evangelism and coordinating labors of lay people throughout several churches.
This system allows for rapid growth, which is good. It also makes a more hierarchical system, with the benefits and drawbacks.
Adventist leaders and Ellen White have strongly advocated that tithe and offerings should be sent to the Conferences in order to fund the work of the ministry. They quote from Malachi to indicate failure to do this is robbing God.
However, some members throughout the time following church organization, have felt they should send their tithe elsewhere to support independent ministries, or to give to people in need, etc. This is especially true if they feel the conference, or even the world SDA church is not acting appropriately, or is compromising doctrine, etc.
If someone is paying tithe then suddenly stops this is often a sign of either changing convictions, or some other issue.
Some independent Adventist ministries may openly encourage people to send their tithe to them. Others may not encourage it, but either don't realize, or might not send it back if they receive it so marked.
There are cooperative independent ministries, that encourage baptism into the SDA church, do not accept tithe, etc. And there are non-coorperative ones who may be quite critical, may accept tithe, etc.
Those who hold to anti-Trinitarian views in the Adventist church tend to be more in tune with the early pioneers, and more prone to favoring non-supportive ministries that advocate the General Conference, etc. have apostasized and the true "remnant of the remnant" should not support them.
So my guess is they can tell which churches are getting into independent ministries based on sudden drops in funds. Some of these upon investigation may deal with issues related to the Godhead.
For a straight-forward North American Division statement on where tithe should go, and how it should not be used for other purposes for independent ministries, see here:
You will find it thoroughly discusses one OT law that Adventists still find applicable.
For a more impassioned appeal expressing the views of the clergy who have to deal with independent ministries, you can read this article from Ministry Magazine, an official magazine of the denomination that goes to ministers:
A Union president shares his views on independent ministries, tithes sent to them, the rumor mills, and how they affect the ministry of the church.
www.ministrymagazine.org
This is older, around 1992, but it gives some of the financial impacts at the time of independent ministry tithe diversion, and the resulting cutting of pastoral staff, enlarging of pastoral districts, etc.
