In the article about the history of the Cyclone Club in the St. Louis Republic on April 21, 1895, it says that the Cyclone grounds at Lafayette Park "were occupied as a camp by General A.J. Smith with a troop of United States soldiers, and the 'Cyclones' became a thing of the past." Based upon the recollections of Leonard Matthews, Ferdinand Garesche and Maurice Alexander, something like that should be easy enough to run down. If it were true then Smith (pictured above) would have seized the grounds sometime in the spring or early summer of 1861. Well...
I can't place Smith in St. Louis until 1869, when he moved to the city and served for a time as postmaster. At the outbreak of the war, it appears that he was out west although he was named chief of cavalry in the Department of Missouri in 1862. That's as close as I can get him in time and place to St. Louis. It's possible that Smith may have moved his command through St. Louis before the Battle of Pilot Knob in 1864 but that's not exactly clear. But there's no way that Smith could have seized Lafayette Park if he was commanding a unit of cavalry in California in 1861.
Tobias has a similar story. The Cyclones "enjoyed the benefit of the grounds for only a brief period as the war of the Rebellion had broken out, soldiers were being recruited and the military powers seized upon it as a fitting spot for an encampment." I think I had kind of merged these two versions in my head and accepted that Tobias' "military powers" was Smith. But that doesn't appear to be the fact.
Louis Gerteis mentions the encampment at Lafayette Park in Civil War St. Louis:
By summer 1861, St. Louis had become the staging ground for federal military operations in the lower Mississippi Valley...The husband of Sarah Hill, a builder by trade, had joined the federal army and served throughout the war as an engineer. She visited him at his camp in Lafayette Park..."Beautiful Lafayette Park," recalled Hill, "with its brilliant flower beds and stretches of green sward, looking like emerald velvet, was turned into a great military camp."
As I mentioned earlier, Smith moved to St. Louis after the war and he lived out the rest of his life in the city. It's likely that Matthews, Alexander and/or Garesche knew him and confused the situation thirty five years after the fact. That's certainly understandable.
The bottom line appears to be that the baseball grounds at Lafayette Park were seized by the military by the summer of 1861. However, it was not done by the order of General A.J. Smith.
In the end, the seizing of the grounds is not as significant to the breakup of the Cyclone Club as is the outbreak of the war itself. By May of 1861 and the Camp Jackson affair, you already have Merritt Griswold and Willie Walker serving with the Union forces in the city, Orville Matthews and Alex Crosman in the United States Navy, Basil Duke undertaking secret missions to arm the pro-Southern Missouri militia, Ed Bredell about to join the Confederate Army and Ferdinand Garesche in a Union military prison. In my mind, Camp Jackson marks the end of the Cyclone Club and it appears that the Union army didn't begin to use Lafayette Park until after that.