Your description of a synchronous process is flawed. A synchronous process has events that update only on the edge of a clock signal (although in this case there is an also an asynchronous reset behaviour )
Your sensitivity list contains more than it needs to describe a synchronous process.
Replace
process(rst, plus, minus, clk, plusin, minusin)
with
process(rst, clk )
signals will then only update when the clock transisitions, or rst changes.
Some compilers are even more picky, and might require you to change
else if rising_edge (clk)then
to
elsif rising_edge(clk) then
EDIT:
This should work. I've layed it out clearly so its actually easy to follow what's going on. I'd suggest you do the same in future. It make simple closure errors easy to spot
entity updown is
port (
signal clk : in std_logic;
signal rst : in std_logic;
signal plus : in std_logic;
signal plusin : in std_logic;
signal minus : in std_logic;
signal minusin : in std_logic;
signal ud_out : out std_logic_vector(3 downto 0);
signal ud_out2 : out std_logic_vector(3 downto 0)
);
end entity updown;
architecture behavioral of updown is
signal s : unsigned (3 downto 0);
signal s2 : unsigned (3 downto 0);
begin
p_counter_process: process(rst, clk)
begin
if rst ='1' then
s <= (others => '0');
s2 <= (others => '0');
elsif rising_edge(clk) then
if plus ='1' or plusin = '1' then
if s = "1001" then
s <= "0000";
if s2 = "1001" then
s2 <= "0000";
else
s2 <= s2 + 1;
end if;
else
s <= s +1;
end if;
end if;
-- you had a mismatched end if statement here. Removed
if minus ='1' or minusin = '1' then
if s = "0000" then
s <= "1001";
if s2= "0000" then
s2 <= "1001";
else
s2 <= s2 - 1;
end if;
else
s <= s - 1;
end if;
end if;
end if;
end process;
ud_out <= std_logic_vector(s);
ud_out2 <= std_logic_vector(s2);
end architecture;