You did the very wisest thing to let these employees go quickly. Because it is true that when they file for unemployment, at this time, it will not be charged to your company. The claims they set up will be (in Texas) usually charged to the earliest of the last five quarters prior to the one we are in. This will set them up for claims based on employers they had prior to working for you. Of course they will use no wages from the current quarter (that you have not reported yet anyway)to set up the claims.
However, in the future, say up to two years from now, if one of these people works again, and is laid off again, and files a new claim for unemployment you will be charged. When claims are filed, they are good for one year from the date filed. After that, the claimant must file a new claim as the old one goes away.
At the time of the new claim, all of the employers in the new "base period" will be charged a percentage of the wages used to set up the claim. Your percentage, since you did not keep these people very long, will be very small, but you will definitely be charged when your wages are in the correct quarters, since you let these people go through no fault of their own. (Incidentally, there is no amount of wages too small to be charged its own percentage of the claim amount, depends on the state how many zeros they put on the percentage .001% of $1)
If you let go five people, there may be one or two of them who may find themselves filing for benfits year after next. If this happens, the tiny amount charged to your account will not be enough to affect your rates very much at all if any. At the present time, employer charge rates are high in most all states due to the economy in general and the state of the states' unemployment trust funds.
Keeping problem employees and then trying to get rid of them after a lengthy period of employment is what causes damage to your unemployment tax rate, because if they are approved for benefits, they have many quarters of pay from your company that you may be charged for.