To reproduce:

            this.radGridView1.Columns.Add("FIRST CELL ID A");

            this.radGridView1.Rows.Add("405-55-214-41763");
            this.radGridView1.Rows.Add("405-55-214-46682");
            this.radGridView1.Rows.Add("405-55-214-46682");

            this.radGridView1.AutoSizeColumnsMode = Telerik.WinControls.UI.GridViewAutoSizeColumnsMode.Fill;
            this.radGridView1.MultiSelect = true;
            this.radGridView1.SelectionMode = Telerik.WinControls.UI.GridViewSelectionMode.CellSelect;

Please refer to the attached gif file illustrating better the text moving. 

Workaround: 
        private void radGridView1_CellFormatting(object sender, Telerik.WinControls.UI.CellFormattingEventArgs e)
        {
            e.CellElement.BorderBottomWidth = 2;
            e.CellElement.BorderRightWidth = 2;
            e.CellElement.BorderTopWidth = 2;
            e.CellElement.BorderLeftWidth = 2;
        }