Once in a while a scrambled tiles issue pops up. Nevertheless, we can't reproduce it on our side. But it seems that, mostly, this could happen when a proxy server is used or there are internet (or other network) connection issues. You can double check if your work systems are making their data transfer with the world wide via a proxy. And also your can see your internet performance.
Also, you can try different tile caching options for the map. By default RadMap uses the built-in .NET caching mechanism and the default request cache level is set to CacheIfAvailable. You can try different levels using the map provider's RequestCacheLevel property and set the IsTileCachingEnabled property to False. Another thing you can try is to manually delete the tiles cache.
string profile = Environment.GetFolderPath(Environment.SpecialFolder.LocalApplicationData);
string cachePath = profile + "\\TelerikMapCache";
Any additional information about your device/network setup could be useful for investigating this.
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